2022/01/28 更新

写真a

マルノ ケンイチ
丸野 健一
所属
理工学術院 基幹理工学部
職名
教授
ホームページ

兼担

  • 理工学術院   大学院基幹理工学研究科

学内研究所等

  • 2020年
    -
    2022年

    理工学術院総合研究所   兼任研究員

学歴

  • 1996年04月
    -
    1999年03月

    九州大学大学院   総合理工学研究科博士課程  

  • 1994年04月
    -
    1996年03月

    九州大学大学院   総合理工学研究科修士課程  

  • 1990年04月
    -
    1994年03月

    大阪府立大学   工学部  

学位

  • 九州大学   博士(理学)

経歴

  • 2017年04月
    -
    継続中

    早稲田大学   理工学術院基幹理工学部応用数理学科   教授

  • 2014年04月
    -
    2017年03月

    早稲田大学   理工学術院基幹理工学部応用数理学科   准教授

  • 2011年09月
    -
    2014年03月

    The University of Texas - Pan American   Associate Professor

  • 2006年09月
    -
    2011年03月

    The University of Texas- Pan American   Assistant Professor

  • 2003年12月
    -
    2006年08月

    九州大学 数理学研究院   COE特任助手

  • 2003年07月
    -
    2003年11月

    コロラド大学   ポスドク研究員

  • 2003年04月
    -
    2003年06月

    オーストラリア国立大学   客員研究員

  • 2000年04月
    -
    2003年03月

    九州大学応用力学研究所   日本学術振興会特別研究員

  • 2001年07月
    -
    2002年11月

    オーストラリア国立大学   客員研究員

  • 1999年04月
    -
    2000年03月

    九州大学応用力学研究所   中核的機関研究員

▼全件表示

所属学協会

  • 2014年
    -
    継続中

    日本流体力学会

  • 2014年
    -
    継続中

    日本応用数理学会

  •  
     
     

    日本物理学会

 

研究分野

  • 応用数学、統計数学   応用数学

  • 数学基礎   応用数学

  • 数理解析学   応用可積分系

研究キーワード

  • 可積分系

  • ソリトン

  • 非線形波動

  • 離散可積分系

  • 水面波

  • 流体力学

  • 数理物理

  • 力学系

  • 数値計算

▼全件表示

論文

  • Pfaffian 解を持つ Hungry Lotka-Volterra 型方程式

    志波 直明, 田中 悠太, 丸野 健一

    津田塾大学数学・計算機科学研究所所報 オンライン研究集会「非線形波動から可積分系へ」(2020)   42   83 - 92  2021年03月

  • 一般的な境界条件での自己適合移動格子スキーム

    丸野 健一, 太田 泰広

    津田塾大学数学・計算機科学研究所所報 オンライン研究集会「非線形波動から可積分系へ」(2020)   42   93 - 102  2021年03月

  • ソリトン方程式の nonlocal reduction と delay reduction

    常松 愛加, 田中 悠太, 丸野 健一

    九州大学応用力学研究所研究集会報告   2019AO-S2   144 - 150  2020年04月

  • BKP 方程式のソリトン解の分類

    田中 悠太, 丸野 健一, 児玉 裕治

    九州大学応用力学研究所研究集会報告   2019AO-S2   31 - 36  2020年04月

  • High-order rogue waves of a long-wave-short-wave model of Newell type

    Junchao Chen, Liangyuan Chen, Bao-Feng Feng, Ken-ichi Maruno

    PHYSICAL REVIEW E   100 ( 5 )  2019年11月

     概要を見る

    The long-wave-short-wave (LWSW) model of Newell type is an integrable model describing the interaction between the gravity wave (long wave) and the capillary wave (short wave) for the surface wave of deep water under certain resonance conditions. In the present paper, we are concerned with rogue-wave solutions to the LWSW model of Newell type. By combining the Hirota's bilinear method and the KP hierarchy reduction, we construct its general rational solution expressed by the determinant. It is found that the fundamental rogue wave for the short wave can be classified into three different patterns: bright, intermediate, and dark states, whereas the one for the long wave is always a bright state. The higher-order rogue wave corresponds to the superposition of fundamental ones. The modulation instability analysis shows that the condition of the baseband modulation instability where an unstable continuous-wave background corresponds to perturbations with infinitesimally small frequencies, coincides with the condition for the existence of rogue-wave solutions.

    DOI

  • KP方程式と結合型KP方程式のソリトン相互作用の解析 (非線形波動現象の数理とその応用)

    田中 悠太, 城戸 真弥, 渡邉 靖之, 丸野 健一, 筧 三郎

    数理解析研究所講究録   ( 2128 ) 141 - 155  2019年09月

    CiNii

  • Isoperimetric deformations of curves on the Minkowski plane

    Hyeongki Park, Jun-ichi Inoguchi, Kenji Kajiwara, Ken-ichi Maruno, Nozomu Matsuura, Yasuhiro Ohta

    INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS   16 ( 7 )  2019年07月

     概要を見る

    We formulate an isoperimetric deformation of curves on the Minkowski plane, which is governed by the defocusing modified Korteweg-de Vries (mKdV) equation. Two classes of exact solutions to the defocusing mKdV equation are also presented in terms of the tau functions. By using one of these classes, we construct an explicit formula for the corresponding motion of curves on the Minkowski plane even though those solutions have singular points. Another class gives regular solutions to the defocusing mKdV equation. Some pictures illustrating the typical dynamics of the curves are presented.

    DOI

  • The interactions of dark line solitons in the Davey-Stewartson II system

    Ken-ichi Maruno, Daichi Suyama, Arata Nagahara

    数理解析研究所講究録   2109   115 - 127  2019年04月

  • General High-order Rogue Waves of the (1+1)-Dimensional Yajima-Oikawa System

    Junchao Chen, Yong Chen, Bao-Feng Feng, Ken-ichi Maruno, Yasuhiro Ohta

    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN   87 ( 9 )  2018年09月

     概要を見る

    General high-order rogue wave solutions for the (1+1)-dimensional Yajima-Oikawa (YO) system are derived by using the Hirota's bilinear method and the KP hierarchy reduction method. These rogue wave solutions are presented in terms of determinants in which the elements are algebraic expressions. The dynamics of first-order and higher-order rogue wave are investigated in details for different values of the free parameters. It is shown that the fundamental (first-order) rogue waves can be classified into three different patterns: bright, intermediate and dark ones. The higher-order rogue waves correspond to the superposition of fundamental rogue waves. Especially, compared with the nonlinear Schrodinger equation, there exists an essential parameter a to control the pattern of rogue wave for both first-order and higher-order rogue waves since the YO system does not possess the Galilean invariance.

    DOI

  • The Derivative Yajima-Oikawa System: Bright, Dark Soliton and Breather Solutions

    Junchao Chen, Bao-Feng Feng, Ken-ichi Maruno, Yasuhiro Ohta

    STUDIES IN APPLIED MATHEMATICS   141 ( 2 ) 145 - 185  2018年08月

     概要を見る

    In this paper, we study the derivative Yajima-Oikawa (YO) system which describes the interaction between long and short waves (SWs). It is shown that the derivative YO system is classified into three types which are similar to the ones of the derivative nonlinear Schrodinger equation. The general N-bright and N-dark soliton solutions in terms of Gram determinants are derived by the combination of the Hirota's bilinear method and the Kadomtsev-Petviashvili hierarchy reduction method. Particularly, it is found that for the dark soliton solution of the SW component, the magnitude of soliton can be larger than the nonzero background for some parameters, which is usually called anti-dark soliton. The asymptotic analysis of two-soliton solutions shows that for both kinds of soliton only elastic collision exists and each soliton results in phase shifts in the long and SWs. In addition, we derive two types of breather solutions from the different reduction, which contain the homoclinic orbit and Kuznetsov-Ma breather solutions as special cases. Moreover, we propose a new (2+1)-dimensional derivative Yajima-Oikawa system and present its soliton and breather solutions.

    DOI

  • Davey-Stewartson 2方程式のダーク型線ソリトン相互作用の理論解析 (非線形波動現象の数理とその応用)

    巣山 大地, 永原 新, 丸野 健一

    数理解析研究所講究録   ( 2076 ) 211 - 223  2018年07月

     概要を見る

    水面波の弱非線形モデルの一つであるDavey-Stewartson(DS)方程式は多様な厳密解を持つことが知られている. 特に, DS2方程式と呼ばれる場合にはダーク型線ソリトン解が存在し, それらが相互作用する多ダーク型線ソリトン解も存在することが知られているが, 多ダーク型線ソリトン相互作用のより詳しい解析はこれまで殆どなされていない. 本稿では, KPソリトン理論を基礎にしたDS2方程式のダーク型線ソリトン相互作用のより詳しい理論解析について報告する.

    CiNii

  • Integrable Discrete Model for One-Dimensional Soil Water Infiltration

    Dimetre Triadis, Philip Broadbridge, Kenji Kajiwara, Ken-ichi Maruno

    STUDIES IN APPLIED MATHEMATICS   140 ( 4 ) 483 - 507  2018年05月

     概要を見る

    We propose an integrable discrete model of one-dimensional soil water infiltration. This model is based on the continuum model by Broadbridge and White, which takes the form of nonlinear convection-diffusion equation with a nonlinear flux boundary condition at the surface. It is transformed to the Burgers equation with a time-dependent flux term by the hodograph transformation. We construct a discrete model preserving the underlying integrability, which is formulated as the self-adaptive moving mesh scheme. The discretization is based on linearizability of the Burgers equation to the linear diffusion equation, but the naive discretization based on the Euler scheme which is often used in the theory of discrete integrable systems does not necessarily give a good numerical scheme. Taking desirable properties of a numerical scheme into account, we propose an alternative discrete model that produces solutions with similar accuracy to direct computation on the original nonlinear equation, but with clear benefits regarding computational cost.

    DOI

  • Jackson の第2 種q-Bessel 関数の精度保証付き数値計算法

    金泉 大介, 丸野 健一

    九州大学応用力学研究所研究集会報告   29AO-S7 ( 1 ) 49 - 54  2018年03月

  • Davey-Stewartson II 方程式のdark型線ソリトン相互作用と三角形分割

    巣山 大地, 永原 新, 丸野 健一

    九州大学応用力学研究所研究集会報告   29AO-S7 ( 1 ) 138 - 144  2018年03月

  • ソリトンとネットワーク

    城戸 真弥, 渡邉 靖之, 田中 悠太, 筧 三郎, 丸野 健一

    九州大学応用力学研究所研究集会報告   29AO-S7 ( 1 ) 131 - 137  2018年03月

  • DKP 方程式のソリトン解のロンスキ型パフィアン表示とネットワーク

    城戸 真弥, 渡邉 靖之, 田中 悠太, 筧 三郎, 丸野 健一

    九州大学応用力学研究所研究集会報告   29AO-S7 ( 1 ) 42 - 48  2018年03月

  • Modified Short Pulse方程式の自己適合移動格子スキーム (非線形波動現象の数理とその応用)

    徐 俊庭, 丸野 健一, Feng Bao-Feng, 太田 泰広

    数理解析研究所講究録   ( 2034 ) 150 - 165  2017年07月

    CiNii

  • An integrable semi-discrete Degasperis-Procesi equation

    Bao-Feng Feng, Ken-ichi Maruno, Yasuhiro Ohta

    NONLINEARITY   30 ( 6 ) 2246 - 2267  2017年06月

     概要を見る

    Based on our previous work on the Degasperis-Procesi equation (Feng et al J. Phys. A: Math. Theor. 46 045205) and the integrable semi-discrete analogue of its short wave limit (Feng et al J. Phys. A: Math. Theor. 48 135203), we derive an integrable semi-discrete Degasperis-Procesi equation by Hirota's bilinear method. Furthermore, N-soliton solution to the semi-discrete Degasperis-Procesi equation is constructed. It is shown that both the proposed semi-discrete Degasperis-Procesi equation, and its N-soliton solution converge to ones of the original Degasperis-Procesi equation in the continuum limit.

    DOI

  • Geometric Formulation and Multi-dark Soliton Solution to the Defocusing Complex Short Pulse Equation

    Bao-Feng Feng, Ken-Ichi Maruno, Yasuhiro Ohta

    STUDIES IN APPLIED MATHEMATICS   138 ( 3 ) 343 - 367  2017年04月

     概要を見る

    In the present paper, we study the defocusing complex short pulse (CSP) equations both geometrically and algebraically. From the geometric point of view, we establish a link of the complex coupled dispersionless (CCD) system with the motion of space curves in Minkowski space R-2,R-1,then with the defocusing CSP equation via a hodograph (reciprocal) transformation, the Lax pair is constructed naturally for the defocusing CSP equation. We also show that the CCD system of both the focusing and defocusing types can be derived from the fundamental forms of surfaces such that their curve flows are formulated. In the second part of the paper, we derive the defocusing CSP equation from the single-component extended Kadomtsev-Petviashvili (KP) hierarchy by the reduction method. As a by-product, the N-dark soliton solution for the defocusing CSP equation in the form of determinants for these equations is provided.

    DOI

  • A two-component generalization of the reduced Ostrovsky equation and its integrable semi-discrete analogue

    Bao-Feng Feng, Ken-ichi Maruno, Yasuhiro Ohta

    JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL   50 ( 5 )  2017年02月

     概要を見る

    In the present paper, we propose a two-component generalization of the reduced Ostrovsky (Vakhnenko) equation, whose differential form can be viewed as the short-wave limit of a two-component Degasperis-Procesi (DP) equation. They are integrable due to the existence of Lax pairs. Moreover, we have shown that the two-component reduced Ostrovsky equation can be reduced from an extended BKP hierarchy with negative flow through a pseudo 3-reduction and a hodograph (reciprocal) transform. As a by-product, its bilinear form and N-soliton solution in terms of pfaffians are presented. One-and two-soliton solutions are provided and analyzed. In the second part of the paper, we start with a modified BKP hierarchy, which is a Backlund transformation of the above extended BKP hierarchy, an integrable semi-discrete analogue of the two-component reduced Ostrovsky equation is constructed by defining an appropriate discrete hodograph transform and dependent variable transformations. In particular, the backward difference form of above semi-discrete two-component reduced Ostrovsky equation gives rise to the integrable semi-discretization of the short wave limit of a two-component DP equation. Their N-soliton solutions in terms of pffafians are also provided.

    DOI

  • The Degasperis-Procesi equation, its short wave model and the CKP hierarchy

    Bao-Feng Feng, Ken-ichi Maruno, Yasuhiro Ohta

    ANNALS OF MATHEMATICAL SCIENCES AND APPLICATIONS   2 ( 2 ) 285 - 316  2017年

     概要を見る

    In the present paper, we show that the Degasperis-Procesi equation and its short-wave model (also known as the reduced-Ostrovsky equation or the Vakhnenko equation) are reductions of C-infinity type two-dimensional Toda-lattices. Bilinear equations are presented to give rise the DP equation and its short-wave model directly through hodograph transformations. As a by-product, the parametric forms of N-soliton solutions are given in terms of pfaffians. One and two-soliton solutions to the DP equation are especially investigated to reveal their properties.

    DOI

  • Davey-Stewartson II 方程式のdark型線ソリトン相互作用 (非線形波動現象の数理に関する最近の進展)

    永原 新, 丸野 健一

    数理解析研究所講究録   ( 1989 ) 94 - 103  2016年04月

    CiNii

  • An integrable semi-discretization of the coupled Yajima-Oikawa system

    Junchao Chen, Yong Chen, Bao-Feng Feng, Ken-ichi Maruno, Yasuhiro Ohta

    JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL   49 ( 16 )  2016年04月

     概要を見る

    An integrable semi-discrete analogue of the one-dimensional coupled Yajima-Oikawa system, which is comprised of multicomponent short waves and one component long wave, is proposed by using a bilinear technique. Based on the reductions of the Backlund transformations of the semi-discrete BKP hierarchy, both the bright and dark soliton solutions in terms of pfaffians are constructed.

    DOI

  • Integrable discretizations and self-adaptive moving mesh method for a coupled short pulse equation

    Bao-Feng Feng, Junchao Chen, Yong Chen, Ken-ichi Maruno, Yasuhiro Ohta

    JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL   48 ( 38 )  2015年09月

     概要を見る

    In the present paper, integrable semi-discrete and fully discrete analogues of a coupled short pulse (CSP) equation are constructed. The key to the construction are the bilinear forms and determinant structure of the solutions of the CSP equation. We also construct N-soliton solutions for the semi-discrete and fully discrete analogues of the CSP equations in the form of Casorati determinants. In the continuous limit, we show that the fully discrete CSP equation converges to the semi-discrete CSP equation, then further to the continuous CSP equation. Moreover, the integrable semi-discretization of the CSP equation is used as a self-adaptive moving mesh method for numerical simulations. The numerical results agree with the analytical results very well.

    DOI

  • Rational solutions to two- and one-dimensional multicomponent Yajima-Oikawa systems

    Junchao Chen, Yong Chen, Bao-Feng Feng, Ken-ichi Maruno

    PHYSICS LETTERS A   379 ( 24-25 ) 1510 - 1519  2015年07月

     概要を見る

    Exact explicit rational solutions of two- and one-dimensional multicomponent Yajima-Oikawa (YO) systems, which contain multi-short-wave components and single long-wave one, are presented by using the bilinear method. For two-dimensional system, the fundamental rational solution first describes the localized lumps, which have three different patterns: bright, intermediate and dark states. Then, rogue waves can be obtained under certain parameter conditions and their behaviors are also classified to above three patterns with different definition. It is shown that the simplest (fundamental) rogue waves are line localized waves which arise from the constant background with a line profile and then disappear into the constant background again. In particular, two-dimensional intermediate and dark counterparts of rogue wave are found with the different parameter requirements. We demonstrate that multirogue waves describe the interaction of several fundamental rogue waves, in which interesting curvy wave patterns appear. in the intermediate times. Different curvy wave patterns form in the interaction of different types fundamental rogue waves. Higher-order rogue waves exhibit the dynamic behaviors that the wave structures start from lump and then retreat back to it, and this transient wave possesses the patterns such as parabolas. Furthermore, different states of higher-order rogue wave result in completely distinguishing lumps and parabolas. Moreover, one-dimensional rogue wave solutions with three states are constructed through the further reduction. Specifically, higher-order rogue wave in one-dimensional case is derived under the parameter constraints. (C) 2015 Elsevier B.V. All rights reserved.

    DOI

  • General Mixed Multi-Soliton Solutions to One-Dimensional Multicomponent Yajima-Oikawa System

    Junchao Chen, Yong Chen, Bao-Feng Feng, Ken-ichi Maruno

    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN   84 ( 7 )  2015年07月

     概要を見る

    In this paper, we derive a general mixed (bright-dark) multi-soliton solution to a one-dimensional multicomponent Yajima-Oikawa (YO) system, i.e., the (M + 1)-component YO system comprised of M-component short waves (SWs) and one-component long wave (LW) for all possible combinations of nonlinearity coefficients including positive, negative and mixed types. With the help of the KP-hierarchy reduction method, we firstly construct two types of general mixed N-soliton solution (two-bright-one-dark soliton and one-bright-two-dark one for SW components) to the (3+1)-component YO system in detail. Then by extending the corresponding analysis to the (M + 1)-component YO system, a general mixed N-soliton solution in Gram determinant form is obtained. The expression of the mixed soliton solution also contains the general all bright and all dark N-soliton solution as special cases. Besides, the dynamical analysis shows that the inelastic collision can only take place among SW components when at least two SW components have bright solitons in mixed type soliton solution. Whereas, the dark solitons in SW components and the bright soliton in LW component always undergo usual elastic collision.

    DOI

  • 非線形波動と自己適合移動格子スキーム (非線形波動現象のメカニズムと数理)

    丸野 健一, 太田 泰広

    数理解析研究所講究録   ( 1946 ) 104 - 117  2015年04月

    CiNii

  • Integrable semi-discretization of a multi-component short pulse equation

    Bao-Feng Feng, Ken-ichi Maruno, Yasuhiro Ohta

    JOURNAL OF MATHEMATICAL PHYSICS   56 ( 4 )  2015年04月

     概要を見る

    In the present paper, we mainly study the integrable semi-discretization of a multicomponent short pulse equation. First, we briefly review the bilinear equations for a multi-component short pulse equation proposed by Matsuno [J. Math. Phys. 52, 123702 (2011)] and reaffirm its N-soliton solution in terms of pfaffians. Then by using a Backlund transformation of the bilinear equations and defining a discrete hodograph (reciprocal) transformation, an integrable semi-discrete multi-component short pulse equation is constructed. Meanwhile, its N-soliton solution in terms of pfaffians is also proved. (C) 2015 AIP Publishing LLC.

    DOI

  • Integrable semi-discretizations of the reduced Ostrovsky equation

    Bao-Feng Feng, Ken-ichi Maruno, Yasuhiro Ohta

    JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL   48 ( 13 ) 135203 - 1--135203-20  2015年04月

     概要を見る

    Based on our previous work on the reduced Ostrovsky equation (J. Phys. A: Math. Theor. 45 355203), we construct its integrable semi-discretizations. Since the reduced Ostrovsky equation admits two alternative representations, one being its original form, the other the differentiated form (the short wave limit of the Degasperis-Procesi equation) two semi-discrete analogues of the reduced Ostrovsky equation are constructed possessing the same N-loop soliton solution. The relationship between these two versions of semi-discretizations is also clarified.

    DOI

  • Multi-Dark Soliton Solutions of the Two-Dimensional Multi-Component Yajima-Oikawa Systems

    Junchao Chen, Yong Chen, Bao-Feng Feng, Ken-ichi Maruno

    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN   84 ( 3 )  2015年03月

     概要を見る

    We present a general form of multi-dark soliton solutions of two-dimensional (2D) multi-component soliton systems. Multi-dark soliton solutions of the 2D and 1D multi-component Yajima-Oikawa (YO) systems, which are often called the 2D and 1D multi-component long wave-short wave resonance interaction systems, are studied in detail. Taking the 2D coupled YO system with two short wave and one long wave components as an example, we derive the general N-dark-dark soliton solution in both the Gram type and Wronski type determinant forms for the 2D coupled YO system via the KP hierarchy reduction method. By imposing certain constraint conditions, the general N-dark-dark soliton solution of the 1D coupled YO system is further obtained. The dynamics of one dark-dark and two dark-dark solitons are analyzed in detail. In contrast with bright-bright soliton collisions, it is shown that dark-dark soliton collisions are elastic and there is no energy exchange among solitons in different components. Moreover, the dark-dark soliton bound states including the stationary and moving ones are discussed. For the stationary case, the bound states exist up to arbitrary order, whereas, for the moving case, only the two-soliton bound state is possible under the condition that the coefficients of nonlinear terms have opposite signs.

    DOI

  • Integrable discretizations of the Dym equation

    Bao-Feng Feng, Jun-ichi Inoguchi, Kenji Kajiwara, Ken-ichi Maruno, Yasuhiro Ohta

    FRONTIERS OF MATHEMATICS IN CHINA   8 ( 5 ) 1017 - 1029  2013年10月

     概要を見る

    Integrable discretizations of the complex and real Dym equations are proposed. N-soliton solutions for both semi-discrete and fully discrete analogues of the complex and real Dym equations are also presented.

    DOI

  • On the tau-functions of the Degasperis-Procesi equation

    Bao-Feng Feng, Ken-ichi Maruno, Yasuhiro Ohta

    JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL   46 ( 4 )  2013年02月

     概要を見る

    The Degasperis-Procesi (DP) equation is investigated from the point of view of determinant-Pfaffian identities. The reciprocal link between the DP equation and the pseudo 3-reduction of the C-infinity two-dimensional Toda system is used to construct the N-soliton solution of the DP equation. The N-soliton solution of the DP equation is presented in the form of Pfaffian through a hodograph (reciprocal) transformation. The bilinear equations, the identities between determinants and Pfaffians, and the tau-functions of the DP equation are obtained from the pseudo 3-reduction of the C-infinity two-dimensional Toda system.

    DOI

  • On the tau-functions of the reduced Ostrovsky equation and the A(2)((2)) two-dimensional Toda system

    Bao-Feng Feng, Ken-ichi Maruno, Yasuhiro Ohta

    JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL   45 ( 35 )  2012年09月

     概要を見る

    The reciprocal link between the reduced Ostrovsky equation and the A(2)((2)) two-dimensional Toda (2D-Toda) system is used to construct the N-soliton solution of the reduced Ostrovsky equation. The N-soliton solution of the reduced Ostrovsky equation is presented in the form of pfaffian through a hodograph (reciprocal) transformation. The bilinear equations and the tau-function of the reduced Ostrovsky equation are obtained from the period 3-reduction of the B-infinity or C-infinity 2D-Toda system, i.e. the A(2)((2)) 2D-Toda system. One of the tau-functions of the A(2)((2)) 2D-Toda system becomes the square of a pfaffian which also becomes a solution of the reduced Ostrovsky equation. There is another bilinear equation which is a member of the 3-reduced extended BKP hierarchy. Using this bilinear equation, we can also construct the same pfaffian solution.

    DOI

  • 水深の浅い領域における2次元ソリトン相互作用 : Benney-Luke方程式とKP方程式

    丸野健一, 児玉裕治, 辻英一, Bao-Feng Feng

    九州大学応用力学研究所研究集会報告   23AO-S7 ( 4 ) 19 - 34  2012年03月

  • Discrete integrable systems and hodograph transformations arising from motions of discrete plane curves

    Bao-Feng Feng, Jun-ichi Inoguchi, Kenji Kajiwara, Ken-ichi Maruno, Yasuhiro Ohta

    JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL   44 ( 39 )  2011年09月

     概要を見る

    We consider integrable discretizations of some soliton equations associated with the motions of plane curves: the Wadati-Konno-Ichikawa elastic beam equation, the complex Dym equation and the short pulse equation. They are related to the modified KdV or the sine-Gordon equations by the hodograph transformations. Based on the observation that the hodograph transformations are regarded as the Euler-Lagrange transformations of the curve motions, we construct the discrete analogues of the hodograph transformations, which yield integrable discretizations of those soliton equations.

    DOI

  • A self-adaptive moving mesh method for the Camassa-Holm equation

    Bao-Feng Feng, Ken-ichi Maruno, Yasuhiro Ohta

    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS   235 ( 1 ) 229 - 243  2010年11月

     概要を見る

    A self-adaptive moving mesh method is proposed for the numerical simulations of the Camassa-olm equation. It is an integrable scheme in the sense that it possesses the exact N-soliton solution. It is named a self-adaptive moving mesh method, because the non-uniform mesh is driven and adapted automatically by the solution. Once the non-uniform mesh is evolved, the solution is determined by solving a tridiagonal linear system. Due to these two superior features of the method, several test problems give very satisfactory results even if by using a small number of grid points. (C) 2010 Published by Elsevier B.V.

    DOI

  • KP2方程式のソリトン解とその応用 (可積分系数理とその応用--RIMS研究集会報告集)

    及川 正行, 辻 英一, 児玉 裕治, 丸野 健一

    数理解析研究所講究録   ( 1700 ) 65 - 84  2010年07月

    CiNii

  • Integrable discretizations of the short pulse equation

    Bao-Feng Feng, Ken-ichi Maruno, Yasuhiro Ohta

    JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL   43 ( 8 )  2010年02月

     概要を見る

    In this paper, we propose integrable semi-discrete and full-discrete analogues of the short pulse (SP) equation. The key construction is the bilinear form and determinant structure of solutions of the SP equation. We also give the determinant formulas of N-soliton solutions of the semi-discrete and full-discrete analogues of the SP equations, from which the multi-loop and multi-breather solutions can be generated. In the continuous limit, the full-discrete SP equation converges to the semi-discrete SP equation, and then to the continuous SP equation. Based on the semi- discrete SP equation, an integrable numerical scheme, i.e. a self-adaptive moving mesh scheme, is proposed and used for the numerical computation of the short pulse equation.

    DOI

  • On the construction of the KP line-solitons and their interactions

    Sarbarish Chakravarty, Tim Lewkow, Ken-Ichi Maruno

    APPLICABLE ANALYSIS   89 ( 4 ) 529 - 545  2010年

     概要を見る

    The line-soliton solutions of the Kadomtsev-Petviashvili (KP) equation are investigated in this article using the -function formalism. In particular, the Wronskian and the Grammian forms of the -function are discussed, and the equivalence of these two forms are established. Furthermore, the interaction properties of two special types of 2-soliton solutions of the KP equation are studied in details.

    DOI

  • The discrete potential Boussinesq equation and its multisoliton solutions

    Ken-Ichi Maruno, Kenji Kajiwara

    APPLICABLE ANALYSIS   89 ( 4 ) 593 - 609  2010年

     概要を見る

    An alternate form of discrete potential Boussinesq (BSQ) equation is proposed and its multisoliton solutions are constructed. An ultradiscrete potential BSQ equation is also obtained from the discrete potential BSQ equation using the ultradiscretization technique. The detail of the multisoliton solutions is discussed by using the reduction technique. The lattice potential BSQ equation derived by Nijhoff et al. is also investigated by using the singularity confinement test. The relation between the proposed alternate discrete potential BSQ equation and the lattice potential BSQ equation by Nijhoff et al. is clarified.

    DOI

  • NOTE ON THE TWO-COMPONENT ANALOGUE OF TWO-DIMENSIONAL LONG WAVE - SHORT WAVE RESONANCE INTERACTION SYSTEM

    Ken-ichi Maruno, Yasuhiro Ohta, Masayuki Oikawa

    GLASGOW MATHEMATICAL JOURNAL   51A   129 - 135  2009年02月

     概要を見る

    An integrable two-component analogue of the two-dimensional long wave - short wave resonance interaction (2c-2d-LSRI) system is studied. Wroliskian solutions of 2c-2d-LSRI system are presented. A reduced case, which describes resonant interaction between an interfacial wave and two surface wave packets a two-layer fluid, is also discussed.

    DOI

  • Determinant and Pfaffian solutions of the strong coupling limit of integrable discrete NLS systems

    Ken-ichi Maruno, Barbara Prinari

    INVERSE PROBLEMS   24 ( 5 )  2008年10月

     概要を見る

    The strong coupling limits of the integrable semi-discrete and fully discrete nonlinear Schrodinger systems are studied by using the Hirota bilinear method. The determinant solutions (in both infinite and finite lattice cases) for the strong coupling limits of semi-discrete and fully discrete nonlinear Schrodinger systems are obtained using a determinant technique. The vector generalizations of the strong coupling limits of semi-discrete and fully discrete nonlinear Schrodinger systems are also presented. The Pfaffian solutions for vector systems are obtained using the Pfaffian technique.

    DOI

  • An integrable semi-discretization of the Camassa-Holm equation and its determinant solution

    Yasuhiro Ohta, Ken-ichi Maruno, Bao-Feng Feng

    JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL   41 ( 35 )  2008年09月

     概要を見る

    An integrable semi-discretization of the Camassa-Holm (CH) equation is presented. The keys of its construction are bilinear forms and determinant structure of solutions of the CH equation. Determinant formulas of N-soliton solutions of the continuous and semi-discrete Camassa-Holm equations are presented. Based on determinant formulas, we can generate multi-soliton, multi-cuspon and multi-soliton-cuspon solutions. Numerical computations using the integrable semi-discrete Camassa-Holm equation are performed. It is shown that the integrable semi-discrete Camassa-Holm equation gives very accurate numerical results even in the cases of cuspon-cuspon and soliton cuspon interactions. The numerical computation for an initial value condition, which is not an exact solution, is also presented.

    DOI

  • Localized solitons of a (2+1)-dimensional nonlocal nonlinear Schrodinger equation

    Ken-ichi Maruno, Yasuhiro Ohta

    PHYSICS LETTERS A   372 ( 24 ) 4446 - 4450  2008年06月

     概要を見る

    An integrable (2 + 1)-dimensional nonlocal nonlinear Schrodinger equation is discussed. The N-soliton solution is given by Gram type determinant. It is found that the localized N-soliton solution has interesting interaction behavior which shows change of amplitude of localized pulses after collisions. Published by Elsevier B.V.

    DOI

  • Integrable discretizations of a two-dimensional Hamiltonian system with a quartic potential

    Bao-Feng Feng, Ken-Ichi Maruno

    INTERNATIONAL JOURNAL OF MODERN PHYSICS B   22 ( 12 ) 1811 - 1822  2008年05月  [査読有り]

     概要を見る

    In this paper, we propose integrable discretizations of a two-dimensional Hamiltonian system with a quartic potential. Using either the method of separation of variables or the method based on bilinear forms, we construct the corresponding integrable mappings for the first three among four integrable cases.

  • Two-component analogue of two-dimensional long wave-short wave resonance interaction equations: a derivation and solutions

    Yasuhiro Ohta, Ken-ichi Maruno, Masayuki Oikawa

    JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL   40 ( 27 ) 7659 - 7672  2007年07月

     概要を見る

    The two- component analogue of two- dimensional long wave - short wave resonance interaction equations is derived in a physical setting. Wronskian solutions of the integrable two- component analogue of two- dimensional long wave - short wave resonance interaction equations are presented.

    DOI

  • Construction of integrals of higher-order mappings

    Ken-ichi Maruno, G. Reinout W. Quispel

    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN   75 ( 12 )  2006年12月  [査読有り]

    DOI

  • Casorati determinant form of dark soliton solutions of the discrete nonlinear Schrodinger equation

    Ken-ichi Maruno, Yasuhiro Ohta

    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN   75 ( 5 )  2006年05月

     概要を見る

    is shown that the N-dark soliton solutions of the integrable discrete nonlinear Schrodinger (IDNLS) equation are given in terms of the Casorati determinant. The conditions for reduction, complex conjugacy, and regularity for the Casorati determinant solution are also given explicitly. The relationship between the IDNLS and the relativistic Toda lattice is discussed.

    DOI

  • N-soliton solutions to the DKP equation and Weyl group actions

    Yuji Kodama, Ken Ichi Maruno

    Journal of Physics A: Mathematical and General   39 ( 15 ) 4063 - 4086  2006年04月

     概要を見る

    We study soliton solutions to the DKP equation which is defined by the Hirota bilinear form, where τ0 ≤ 1. The τ-functions τn are given by the Pfaffians of a certain skew-symmetric matrix. We identify a one-soliton solution as an element of the Weyl group of D-type, and discuss a general structure of the interaction patterns among the solitons. Soliton solutions are characterized by a 4N × 4N skew-symmetric constant matrix which we call the B-matrix. We then find that one can have M-soliton solutions with M being any number from N to 2N - 1 for some of the 4N × 4N B-matrices having only 2N nonzero entries in the upper-triangular part (the number of solitons obtained from those B-matrices was previously expected to be just N). © 2006 IOP Publishing Ltd.

    DOI

  • Dissipative solitons of the discrete complex cubic-quintic Ginzburg-Landau equation

    Ken Ichi Maruno, Adrian Ankiewicz, Nail Akhmediev

    Physics Letters, Section A: General, Atomic and Solid State Physics   347 ( 4-6 ) 231 - 240  2005年12月

     概要を見る

    We study, analytically, the discrete complex cubic-quintic Ginzburg-Landau (dCCQGL) equation with a non-local quintic term. We find a set of exact solutions which includes, as particular cases, bright and dark soliton solutions, constant magnitude solutions with phase shifts, periodic solutions in terms of elliptic Jacobi functions in general forms, and various particular periodic solutions. © 2005 Elsevier B.V. All rights reserved.

    DOI

  • Resonance and web structure in discrete soliton systems: The two-dimensional Toda lattice and its fully discrete and ultra-discrete analogues

    Ken Ichi Maruno, Gino Biondini

    Journal of Physics A: Mathematical and General   37 ( 49 ) 11819 - 11839  2004年12月

     概要を見る

    We present a class of solutions of the two-dimensional Toda lattice equation, its fully discrete analogue and its ultra-discrete limit. These solutions demonstrate the existence of soliton resonance and web-like structure in discrete integrable systems such as differential-difference equations, difference equations and cellular automata (ultra-discrete equations).

    DOI

  • Complexiton solutions of the Toda lattice equation

    Wen Xiu Ma, Ken ichi Maruno

    Physica A: Statistical Mechanics and its Applications   343 ( 1-4 ) 219 - 237  2004年11月

     概要を見る

    A set of coupled conditions consisting of differential-difference equations is presented for Casorati determinants to solve the Toda lattice equation. One class of the resulting conditions leads to an approach for constructing complexiton solutions to the Toda lattice equation through the Casoratian formulation. An analysis is made for solving the resulting system of differential-difference equations, thereby providing the general solution yielding eigenfunctions required for forming complexitons. Moreover, a feasible way is presented to compute the required eigenfunctions, along with examples of real complexitons of lower order. © 2004 Elsevier B.V. All rights reserved.

    DOI

  • Generalized Casorati determinant and positon-negaton-type solutions of the Toda lattice equation

    Ken Ichi Maruno, Wen Xiu Ma, Masayuki Oikawa

    Journal of the Physical Society of Japan   73 ( 4 ) 831 - 837  2004年04月

     概要を見る

    A set of conditions is presented for Casorati determinants to give solutions to the Toda lattice equation. It is used to establish a relation between the Casorati determinant solutions and the generalized Casorati determinant solutions. Positons, negatons and their interaction solutions of the Toda lattice equation are constructed through the generalized Casorati determinant technique. A careful analysis is also made for general positons and negatons, the resulting positons and negatons of order one being explicitly computed. The generalized Casorati determinant formulation for the two dimensional Toda lattice (2dTL) equation is presented. It is shown that positon, negaton and complexiton type solutions in the 2dTL equation exist and these solutions reduce to positon, negaton and complexiton type solutions in the Toda lattice equation by the standard reduction procedure. ©2004 The Physical Society of Japan.

    DOI

  • Exact localized and periodic solutions of the discrete complex Ginzburg-Landau equation

    Ken ichi Maruno, Adrian Ankiewicz, Nail Akhmediev

    Optics Communications   221 ( 1-3 ) 199 - 209  2003年06月

     概要を見る

    We study, analytically, the discrete complex cubic Ginzburg-Landau (dCCGL) equation. We derive the energy balance equation for the dCCGL and consider various limiting cases. We have found a set of exact solutions which includes as particular cases periodic solutions in terms of elliptic Jacobi functions, bright and dark soliton solutions, and constant magnitude solutions with phase shifts. We have also found the range of parameters where each exact solution exists. We discuss the common features of these solutions and solutions of the continuous complex Ginzburg-Landau model and solutions of Hamiltonian discrete systems and also their differences. © 2003 Elsevier Science B.V. All rights reserved.

    DOI

  • Exact localized solutions of quintic discrete nonlinear Schrödinger equation

    Ken Ichi Maruno, Yasuhiro Ohta, Nalini Joshi

    Physics Letters, Section A: General, Atomic and Solid State Physics   311 ( 2-3 ) 214 - 220  2003年05月

     概要を見る

    We study a new quintic discrete nonlinear Schrödinger (QDNLS) equation which reduces naturally to an interesting symmetric difference equation of the form φn+1 + φn-1 = F(φn). Integrability of the symmetric mapping is checked by singularity confinement criteria and growth properties. Some new exact localized solutions for integrable cases are presented for certain sets of parameters. Although these exact localized solutions represent only a small subset of the large variety of possible solutions admitted by the QDNLS equation, those solutions presented here are the first example of exact localized solutions of the QDNLS equation. We also find chaotic behavior for certain parameters of nonintegrable case. © 2003 Elsevier Science B.V. All rights reserved.

    DOI

  • Swift-Hohenberg型方程式の厳密解の安定性について (非線形波動現象の数理とその応用 研究集会報告集)

    及川 正行, 丸野 健一, Ankiewicz A., Akhmediev N.

    数理解析研究所講究録   ( 1311 ) 140 - 145  2003年04月

    CiNii

  • Periodic and optical soliton solutions of the quintic complex Swift-Hohenberg equation

    Adrian Ankiewicz, Ken ichi Maruno, Nail Akhmediev

    Physics Letters, Section A: General, Atomic and Solid State Physics   308 ( 5-6 ) 397 - 404  2003年03月

     概要を見る

    Using a direct ansatz approach, we have found a number of periodic zero-velocity analytic solutions of the complex quintic Swift-Hohenberg equation (CSHE). These find application in assorted optical problems. Particular cases of periodic solutions, where the elliptic function modulus equals 1, are various localized solutions of the CSHE. Each of these solutions exists for a certain relation between the parameters of the equation. As a result, they are particular cases of the complete set of periodic and localised solutions which may exist for this equation. In fact, they are multi-parameter families of solutions and they can serve as a seeding set of solutions which could be useful in other optical studies. We have also derived energy and momentum balance equations for the solutions of CSHE and checked that our stationary solutions satisfy the energy balance equation. © 2003 Elsevier Science B.V. All rights reserved.

    DOI

  • Exact soliton solutions of the one-dimensional complex Swift-Hohenberg equation

    Ken Ichi Maruno, Adrian Ankiewicz, Nail Akhmediev

    Physica D: Nonlinear Phenomena   176 ( 1-2 ) 44 - 66  2003年02月

     概要を見る

    Using Painlevé analysis, the Hirota multi-linear method and a direct ansatz technique, we study analytic solutions of the (1+1)-dimensional complex cubic and quintic Swift-Hohenberg equations. We consider both standard and generalized versions of these equations. We have found that a number of exact solutions exist to each of these equations, provided that the coefficients are constrained by certain relations. The set of solutions include particular types of solitary wave solutions, hole (dark soliton) solutions and periodic solutions in terms of elliptic Jacobi functions and the Weierstrass ℘ function. Although these solutions represent only a small subset of the large variety of possible solutions admitted by the complex cubic and quintic Swift-Hohenberg equations, those presented here are the first examples of exact analytic solutions found thus far. © 2002 Elsevier Science B.V. All rights reserved.

    DOI

  • Dissipative solitons in discrete systems

    Kenichi Maruno, Adrian Ankiewicz, Nail Akhmediev

    Pacific Rim Conference on Lasers and Electro-Optics, CLEO - Technical Digest   1   242  2003年

     概要を見る

    © 2003 IEEE. We study, analytically, the discrete complex cubic Ginzburg-Landau (dCCGL) equation. We have found a set of exact solutions which includes bright and dark soliton solutions,

    DOI

  • Bilinear forms of integrable lattices related to Toda and Lotka-Volterra lattices

    Ken Ichi Maruno, Wen Xiu Ma

    Journal of Nonlinear Mathematical Physics   9   127 - 139  2002年

     概要を見る

    Copyright © 2002 by K Maruno and W X Ma. Hirota's bilinear technique is applied to some integrable lattice systems related to the Bäcklund transformations of the 2DToda, Lotka-Volterra and relativistic Lotka- Volterra lattice systems, which include the modified Lotka-Volterra lattice system, the modified relativistic Lotka-Volterra lattice system, and the generalized Blaszak- Marciniak lattice systems. Determinant solutions are constructed through the resulting bilinear forms, especially for the modified relativistic Lotka-Volterra lattice system and a two-dimensional Blaszak-Marciniak lattice system.

    DOI

  • Bilinear structure and determinant solution for the relativistic Lotka-Volterra equation

    Ken ichi Maruno, Masayuki Oikawa

    Physics Letters, Section A: General, Atomic and Solid State Physics   270 ( 3-4 ) 122 - 131  2000年05月

     概要を見る

    The relativistic Lotka-Volterra (RLV) lattice and the discrete-time relativistic Lotka-Volterra (dRLV) lattice are investigated by using the bilinear formalism. The bilinear equations for them are systematically constructed with the aid of the singularity confinement test. It is shown that the RLV lattice and dRLV lattice are decomposed into the Backlund transformations of the Toda lattice system. The N-soliton solutions are explicitly constructed in the form of the Casorati determinant. (C) 2000 Elsevier Science B.V.

    DOI

  • Bilinearization of discrete soliton equations through the singularity confinement test

    Kenji Kajiwara, Ken Ichi Maruno, Masayuki Oikawa

    Chaos, solitons and fractals   11 ( 1 ) 33 - 39  2000年

     概要を見る

    Bilinear equations can be obtained for discrete soliton equations using the singularity confinement test. This shows that the singularity confinement test is useful for detecting integrability and in constructing solutions. Thus, the singularity confinement test is truly a powerful tool for studying discrete integrable systems.

    DOI

  • 特異点閉じ込め法と広田の方法 (離散可積分系の応用数理)

    丸野 健一

    数理解析研究所講究録   ( 1098 ) 70 - 81  1999年04月

    CiNii

  • Casorati determinant solution for the discrete-time relativistic Toda lattice equation

    Ken Ichi Maruno, Kenji Kajiwara, Masayuki Oikawa

    Physics Letters, Section A: General, Atomic and Solid State Physics   241 ( 6 ) 335 - 343  1998年05月

     概要を見る

    The discrete-time relativistic Toda lattice (dRTL) equation is investigated by using the bilinear formalism. Bilinear equations are systematically constructed with the aid of the singularity confinement method. It is shown that the dRTL equation is decomposed into the Bäcklund transformations of the discrete-time Toda lattice equation. The N-soliton solution is explicitly constructed in the form of the Casorati determinant. © 1998 Published by Elsevier Science B.V.

    DOI

  • Bilinearization of discrete soliton equations and singularity confinement

    Kenichi Maruno, Kenji Kajiwara, Shinichiro Nakao, Masayuki Oikawa

    Physics Letters, Section A: General, Atomic and Solid State Physics   229 ( 3 ) 173 - 182  1997年05月

     概要を見る

    The singularity confinement method is applied to the systematic derivation of the bilinear equations for discrete soliton equations. Using the bilinear forms, the N-soliton and algebraic solutions of the discrete potential mKdV equation are constructed. © 1997 Published by Elsevier Science B.V.

    DOI

  • 密度成層キャビティ流における混合層の発達

    馬場 信弘, 木村 茂, 池田 義行, 丸野 健一, 平野 進, 高松 健一郎

    関西造船協会誌   222   225 - 230  1994年

     概要を見る

    The mixing process in stratified fluid in the closed region of the ocean by the recirculating flow induced by wind is modelled in the laboratory using the lid-driven cavity flow. The deepening of a mixed layer into a region of constant density gradient is examined and the three-dimensional features of flow structures near a density interface is investigated by visualization experiments. The characteristics of the mixed layer and the stratified layer are determined using a conductivity probe. The flow pattern of a primary circulation formed in the top downstream corner, growing gradually, but bounded by a stratified fluid beneath as it were a wall is quite different from that of homogeneous fluid. The density interface formed by erosion of the basic density gradient is distorted by the primary circulation and at the same time it is subject to the three-dimensional instability in the initial stage of the formation. Then the interface is of a wave shape in the spanwise direction, sharper near the crests and flatter in troughs, the wave length of which increases as the interface descends. It is shown that this is caused by the existence of the vortical structure which consists of the pairs of counter-rotating wise stream vortices in the strong shear layer near the interface. The considerable amount of the spanwise distortion of the interface indicates that the three-dimensional structure possibly makes a significant contribution to the mixing across the density interface along with the primary circulation in the upper layer.

    DOI CiNii

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共同研究・競争的資金等の研究課題

  • 海洋における大振幅・非線形波動の数理モデルと解析

    日本学術振興会  科学研究費助成事業 基盤研究(B)

    研究期間:

    2017年04月
    -
    2022年03月
     

    村重 淳, 片岡 武, 井口 達雄, 柿沼 太郎, 丸野 健一

     概要を見る

    本研究の目的は,海洋における大振幅波動の本質(非線形性と分散性)をとらえた数学モデルを導出し,その数理解析を行うことである.平成30年度(2年目)は以下の三つの研究テーマについて実施計画を立て,3月末の報告会(栃木県那須)で進捗状況を確認した.研究成果は,発表論文 22 件(査読有 10 件,国際共著 4 件),学会発表 38 件(招待講演 11 件,国際講演 19 件)で公表されている.研究内容の概要は以下の通りである..
    1. 数学モデル: (1) Isobe-Kakinuma モデルの数学的正当性を厳密に評価し,従来のモデルとの比較により長所を示した(井口).(2) 2次元Benney-Luke方程式の線状孤立波解の安定性を調べた(水町).
    2. 内部波:(1) 2層流体の界面で発生する内部孤立波が大陸棚を通過するときの挙動を Isobe-Kakinuma モデルを用いて数値的に調べた(柿沼),(2)一様成層流体中を伝播する内部波の反射により発生する平均流について理論的・数値的に解析したた(片岡).
    3. 大振幅・非線形波動の数値計算:(1) シアー流上の深水波の安定性を複素解析の手法を用いて数値的に調べた(村重).(2) 自己適合移動格子法を用いた大振幅非線形波動の計算法の有効性を示した(丸野),(3) 砕波のシミュレーションにおける空気の運動の重要性を調べた(日野),(4) 流体の運動方程式の重要な構造を保存する離散化法を提案した(太田).
    また,国際研究集会 Workshop on Nonlinear Water Waves を平成30年5月22日~26日に京都大学数理解析研究所で開催し,活発な議論が交わされた(参加者:約40名,海外からの招待講演者:8名).研究集会の成果として,講演に基づいた論文集を発行した(印刷中).

  • 可積分系の離散的方法を基盤とした非線形波動解析のための計算アルゴリズムの開発

    日本学術振興会  科学研究費助成事業 基盤研究(C)

    研究期間:

    2018年04月
    -
    2021年03月
     

    丸野 健一, 太田 泰広, 筧 三郎

     概要を見る

    可積分系の研究において見出された離散数理構造を積極的に用いて複雑な波動現象解明のための革新的な計算手法を開発することを目標として研究を行なった。具体的には、(1) 離散可積分系研究で見出された手法を基盤とした高精度で高速な構造保存型差分スキームの開発およびその数理的性質の研究、(2) 2次元波動パターンのある時刻における情報からそのパターンを生成する厳密解を構成し波動パターンの時間発展を予測する計算アルゴリズムの開発に取り組んだ。(1)においては離散可積分系の手法とともに離散微分幾何学の手法を積極的に用いて、申請者らが提案した自己適合移動格子スキームの研究、開発を中心に行なった。いくつかの物理現象の数理モデルに対して自己適合移動格子スキームの構築と精度検証を行なった。また、離散微分幾何学的アプローチを用いて離散空間曲線の運動から渦糸の運動を記述する複素WKI方程式の自己適合移動格子スキームの構築に取り組んだ。この結果については現在論文を執筆中であり国際査読論文誌に投稿予定である。(2)においては、2次元可積分系理論を基盤としてコード図、ネットワーク図、三角形分割などの組み合わせ論や計算幾何学の手法を積極的に用いて2次元非線形波動方程式の分類問題に取り組んだ。特に、DKP(結合型KP)方程式、Davey-Stewartson方程式のソリトンが作るパターンの分類手法の開発に取り組み、ネットワーク図、コード図の拡張にたどり着いた。またこれまで困難であったBKP方程式のソリトンパターンの研究についても前進があった。現在、これらの成果をまとめて論文を執筆中で国際査読論文誌に投稿予定である。
    離散可積分系の国際会議「Symmetries and Integrability of Difference Equations」を11月に福岡で開催した。

  • 離散微分幾何に基づく離散時間幾何モデルの構築

    日本学術振興会  科学研究費助成事業 挑戦的萌芽研究

    研究期間:

    2016年04月
    -
    2018年03月
     

    梶原 健司, 丸野 健一, 筧 三郎, 廣瀬 三平

     概要を見る

    本研究では(a)伸縮や外力を伴う曲線変形の離散モデル,(b)界面の変形の離散時間モデル,(c)1次元弾性体の離散モデルの研究を進めた.(a)では曲線短縮方程式の新しい離散モデルと離散局所誘導方程式の構築に成功した.(b)ではHele-Shaw流を記述する複素Dym方程式の双線形化に成功,また土壌中の水浸透に関するBroadbridge-Whiteモデルの離散化と数値計算に成功した.(c)についてはオイラーの弾性曲線の可積分離散モデルの離散変分原理による定式化に成功し,さらに相似幾何における弾性曲線が設計工学で使われる対数型美的曲線に他ならないことを示し,その一般化に対する数学的基盤を与えた.

  • 可積分系理論を基盤とした大変形現象の数値計算のための自己適合移動格子法の開発

    日本学術振興会  科学研究費助成事業 基盤研究(C)

    研究期間:

    2015年04月
    -
    2018年03月
     

    丸野 健一, 太田 泰広, 高橋 大輔

     概要を見る

    大振幅非線形波動を記述する偏微分方程式の解の構造を保存する差分スキームの構築法の確立とその数値計算法への応用に向けて、これまで離散化に成功していなかったタイプの非線形波動方程式(多成分系、3次元渦糸問題、水面波の数理モデル、水の土壌への浸透を記述する数理モデルなど)の解の構造を保存する離散化を行い、様々な方程式に対して自己適合移動格子スキームを構築することに成功した。さらに、それらを用いた数値計算の精度の検証を行い、自己適合移動格子スキームの有効性を示した。また、自己適合移動格子スキームと離散微分幾何学との関係についても詳しく調べた。

  • 高次元ソリトン方程式が生成する波動パターンの数理解析

    日本学術振興会  科学研究費助成事業 若手研究(B)

    研究期間:

    2006年
     
     
     

    丸野 健一

  • 非線形離散方程式の可積分性判定テストと厳密解の構成法

    日本学術振興会  科学研究費助成事業 特別研究員奨励費

    研究期間:

    2000年
    -
    2002年
     

    丸野 健一

     概要を見る

    可積分系のもつ特徴として、パンルベ性という性質が広く知られており、この性質を利用して可積分性を判定するテストとしてパンルベテストがある。差分方程式版のパンルベ性が特異点閉じ込めの性質であり、非線形差分方程式の可積分性を判定する方法として提案されたのが特異点閉じ込めテストである。パンルベ性、特異点閉じ込めの性質は、方程式の可積分性を判定することにのみ有効であるわけではなく、解の構成にも大きな威力を発揮することが、多くの研究によって示されている。本研究では、パンルベテスト、特異点閉じ込めテストの応用を試み、非線形方程式を解析することを目的としている。
    今年度得た主な結果は以下のとおりである。
    1.パターン形成などの分野で注目されているComplex Swift-Hohenberg方程式にパンルベテストを適用し、その結果を利用して多重線形形式に変換し、広田の方法によって厳密解を具体的に与えた。これは非線形光学などの物理において、大変重要な役割をすると考えられる。
    2.Complex quintic Swift-Hohenberg方程式の非線形光学での応用を考え、様々な厳密解を導出した。また、厳密解を用いてエネルギーについての解析を行った。
    3.新しい離散型非線形シュレーディンガー方程式を提案し、その厳密解と非線形写像について特異点閉じ込めテストを用いて解析した。この方程式は光現象を記述するものであり、今後、重要な役割をするものと予想される。
    4.波長多重の光ソリトンを記述する結合型非線形シュレーディンガー方程式についての解析を行った。具体的には高次のソリトン解と呼ばれるものの導出を目指しているが、その準備として、非線形シュレーディンガー方程式の高次のソリトン解を双線形化法の立場から整理した。

▼全件表示

講演・口頭発表等

  • パフィアン解を持つ Hungry Lotka-Volterra 型方程式のソリトン相互作用

    志波 直明, 田中 悠太, 中田 健太, 丸野 健一

    オンライン研究集会「非線形波動と可積分系」  

    発表年月: 2021年11月

    開催年月:
    2021年11月
     
     
  • N ソリトン解を持つ遅延ソリトン方程式の構成法

    中田 健太, 丸野 健一

    オンライン研究集会「非線形波動と可積分系」  

    発表年月: 2021年11月

    開催年月:
    2021年11月
     
     
  • Pfaffian解を持つHungry Lotka-Volterra型方程式とソリトン解

    志波 直明, 田中 悠太, 中田 健太, 丸野 健一

    日本応用数理学会2021年度年会  

    発表年月: 2021年09月

    開催年月:
    2021年09月
     
     
  • 自己適合移動格子スキームの最近の進展

    丸野 健一  [招待有り]

    研究集会「非線形海洋波の数理とその応用」  

    発表年月: 2021年03月

    開催年月:
    2021年03月
     
     
  • 一般的な境界条件での自己適合移動格子スキームと数値計算

    丸野 健一, 太田 泰広

    日本物理学会第76回年次大会  

    発表年月: 2021年03月

    開催年月:
    2021年03月
     
     
  • 多ソリトン解を持つ可積分系の遅延化

    中田 健太, 丸野 健一

    日本応用数理学会第17回研究部会連合発表会  

    発表年月: 2021年03月

    開催年月:
    2021年03月
     
     
  • SIR モデルの解構造を保存する離散化と厳密解

    丸野 健一, 田中 悠太

    日本応用数理学会第17回研究部会連合発表会  

    発表年月: 2021年03月

    開催年月:
    2021年03月
     
     
  • Pfaffian 解を持つ Hungry Lotka-Volterra 型方程式

    志波 直明, 田中 悠太, 丸野 健一

    オンライン研究集会「非線形波動から可積分系へ」津田塾大学数学計算機科学研究所  

    発表年月: 2020年11月

    開催年月:
    2020年11月
     
     
  • 一般的な境界条件での自己適合移動格子スキーム

    丸野 健一, 太田 泰広

    オンライン研究集会「非線形波動から可積分系へ」津田塾大学数学計算機科学研究所  

    発表年月: 2020年11月

    開催年月:
    2020年11月
     
     
  • Integrable discretization of soliton equations and numerical computations

    Ken-ichi Maruno  [招待有り]

    2019 28th Annual Workshop on Differential Equations, Academia Sinica, Taiwan  

    発表年月: 2019年12月

    開催年月:
    2019年12月
     
     
  • Numerical and analytical studies of the KP I equation

    Ken-ichi Maruno  [招待有り]

    Mini Symposium on Integrable Systems, Academia Sinica, Taiwan  

    発表年月: 2019年12月

    開催年月:
    2019年12月
     
     
  • 自己適合移動格子スキームの境界条件

    丸野 健一

    研究集会「非線形波動研究の多様性」九州大学応用力学研究所  

    発表年月: 2019年10月

    開催年月:
    2019年10月
    -
    2019年11月
  • 田中 悠太; 丸野 健一; 児玉 裕治

    BKP方程式のソリトン解の分類

    研究集会「非線形波動研究の多様性」九州大学応用力学研究所  

    発表年月: 2019年10月

    開催年月:
    2019年10月
    -
    2019年11月
  • Soliton solutions of the DKP equation and networks

    Yuta Tanaka, Shinya Kido, Yasuyuki Watanabe, Ken-ichi Maruno, Saburo Kakei

    China-Japan Joint Workshop on Integrable Systems 2019, 湘南国際村センター  

    発表年月: 2019年08月

    開催年月:
    2019年08月
     
     
  • Construction of exact soliton solutions in the spinor F = 1 Bose-Einstein condensates

    Haoyu Yang, Yuta Tanaka, Ken-ichi Maruno

    China-Japan Joint Workshop on Integrable Systems 2019, 湘南国際村センター  

    発表年月: 2019年08月

    開催年月:
    2019年08月
     
     
  • Integrable discretizations of the complex WKI equation and numerical computation of a vortex filament

    Ken-ichi Maruno

    ICIAM2019, Universitat de Valencia, Valencia Spain  

    発表年月: 2019年07月

    開催年月:
    2019年07月
     
     
  • Integrable discretizations of the complex WKI equation: numerical computation of a vortex filament

    Ken-ichi Maruno

    ISLAND V: Integrable systems, special functions and combinatorics, the Gaelic College, UK  

    発表年月: 2019年06月

    開催年月:
    2019年06月
     
     
  • Integrable discretizations of integrable systems and motion of discrete curves

    Ken-ichi Maruno

    The 2nd JNMP Conference on Nonlinear Mathematical Physics, University of Santiago, Chile  

    発表年月: 2019年05月

    開催年月:
    2019年05月
    -
    2019年06月
  • 自己適合移動格子スキームと離散曲線

    丸野健一  [招待有り]

    研究集会「非線形海洋波の数理の最近の進展」, ホテルサンバレー那須  

    発表年月: 2019年03月

    開催年月:
    2019年03月
     
     
  • An integrable discretization of the complex WKI equation and a vortex filament

    Ken-ichi Maruno, Shinya Kido, Satomi Nakamura  [招待有り]

    AMS Spring Central and Western Joint Sectional Meeting, University of Hawaii at Manoa, Honolulu, Hawaii, USA  

    発表年月: 2019年03月

    開催年月:
    2019年03月
     
     
  • BKP方程式のGram型Pfaffian解とそのソリトン相互作用

    田中悠太, 丸野健一, 児玉裕治

    日本応用数理学会2019年研究部会連合発表会, 筑波大学  

    発表年月: 2019年03月

    開催年月:
    2019年03月
     
     
  • Soliton interactions of the KP and DKP equations and their network diagrams

    Ken-ichi Maruno  [招待有り]

    JSPS Almuni Association Seminar, University of Texas Rio Grande Valley, Edinbuburg, Texas, USA  

    発表年月: 2018年12月

    開催年月:
    2018年11月
    -
    2018年12月
  • KP方程式と結合型KP方程式のソリトン相互作用の解析

    田中 悠太, 城戸 真弥, 渡邉 靖之, 丸野 健一, 筧 三郎

    非線形波動現象の数理とその応用,京都大学数理解析研究所  

    発表年月: 2018年10月

    開催年月:
    2018年10月
     
     
  • DKP solitons and networks

    Ken-ichi Maruno  [招待有り]

    The 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications, National Taiwan University, Taipei, Taiwan  

    発表年月: 2018年07月

    開催年月:
    2018年07月
     
     
  • The interactions of dark line solitons in the Davey-Stewartson II system

    Ken-ichi Maruno  [招待有り]

    Workshop on Nonlinear Water Waves, 京都大学数理解析研究所  

    発表年月: 2018年05月

    開催年月:
    2018年05月
     
     
  • Discrete structures of integrable systems and its applications

    Ken-ichi Maruno

    2018 ICIAM Workshop, Drexel University, Philadelphia, USA  

    発表年月: 2018年05月

    開催年月:
    2018年05月
     
     
  • DKP方程式のソリトン解のロンスキ型パフィアン表示に関するネットワークを用いた解析

    城戸 真弥, 田中 悠太, 渡邉 靖之, 丸野 健一, 筧 三郎

    日本応用数理学会第14回研究部会連合発表会, 大阪大学吹田キャンパス  

    発表年月: 2018年03月

    開催年月:
    2018年03月
     
     
  • 乗積公式と積分によるq-gamma関数の精度保証付き数値計算

    金泉 大介, 丸野 健一

    2017年度応用数学合同研究集会, 龍谷大学瀬田キャンパス , 龍谷大学瀬田キャンパス  

    発表年月: 2017年12月

    開催年月:
    2017年12月
     
     
  • DKP方程式のソリトン解とネットワーク

    城戸 真弥, 田中 悠太, 渡邉 靖之, 筧 三郎, 丸野 健一

    2017年度応用数学合同研究集会, 龍谷大学瀬田キャンパス  

    発表年月: 2017年12月

    開催年月:
    2017年12月
     
     
  • Jacksonの第2種q-Bessel関数の精度保証付き数値計算

    金泉 大介, 丸野 健一

    研究集会「 非線形波動の新潮流-理論とその応用-」九州大学応用力学研究所  

    発表年月: 2017年11月

    開催年月:
    2017年11月
     
     
  • Davey-StewartsonⅡ方程式のダーク型線ソリトン相互作用と三角形分割

    巣山 大地, 永原 新, 丸野 健一

    研究集会「 非線形波動の新潮流-理論とその応用-」九州大学応用力学研究所  

    発表年月: 2017年11月

    開催年月:
    2017年11月
     
     
  • ソリトンとネットワーク

    城戸 真弥, 田中 悠太, 渡邉 靖之, 筧 三郎, 丸野 健一

    研究集会「 非線形波動の新潮流-理論とその応用-」九州大学応用力学研究所  

    発表年月: 2017年11月

    開催年月:
    2017年11月
     
     
  • DKP方程式のソリトン解とネットワーク

    渡邉 靖之, 田中 悠太, 城戸 真弥, 筧 三郎, 丸野 健一

    研究集会「 非線形波動の新潮流-理論とその応用-」 九州大学応用力学研究所  

    発表年月: 2017年11月

    開催年月:
    2017年11月
     
     
  • Davey-Stewartson2方程式のダーク型線ソリトン相互作用の理論解析

    巣山 大地, 永原 新, 丸野 健一

    研究集会「非線形波動現象の数理とその応用」 京都大学数理解析研究所  

    発表年月: 2017年10月

    開催年月:
    2017年10月
     
     
  • q-Bessel関数の積分表示とq-超幾何関数を用いる精度保証付き数値計算法

    金泉大介, 丸野健一

    日本応用数理学会2017年度年会, 武蔵野大学有明キャンパス  

    発表年月: 2017年09月

    開催年月:
    2017年09月
     
     
  • q-Bessel関数とq-Airy関数の精度保証付き数値計算

    金泉大介, 丸野健一

    第46回数値解析シンポジウム  

    発表年月: 2017年06月

    開催年月:
    2017年06月
     
     
  • Integrable self-adaptive moving mesh scheme for the modified short pulse equation

    Ken-ichi Maruno

    Physics and Mathematics of Nonlinear Phenomena PMNP2017: 50 years of IST, Gallipori, Italy  

    発表年月: 2017年06月

    開催年月:
    2017年06月
     
     
  • 可積分系と数値計算:厳密解 vs. 数値解

    丸野 健一  [招待有り]

    研究集会「可積分系の数理と応用」 京都大学数理解析研究所  

    発表年月: 2017年09月

    開催年月:
    2017年09月
    -
    2017年

▼全件表示

特定課題研究

  • 自己適合移動格子スキームの開発・改良と離散微分幾何学の応用

    2014年  

     概要を見る

    渦糸の運動を記述する局所誘導方程式と複素WKI方程式のつながり(ホドグラフ変換)に着目し,複素WKI方程式の可積分性を保つ離散化を行い,渦糸に対する自己適合移動格子スキームを構築した.これを用いて渦糸の数値計算を高速かつ精度よく計算することに成功した.これは3次元空間問題における初の自己適合移動格子スキームである.

 

現在担当している科目

▼全件表示

担当経験のある科目(授業)

  • Numerical Analysis and Simulation

    早稲田大学  

    2020年09月
    -
    継続中
     

  • 常微分方程式入門

    早稲田大学  

    2020年04月
    -
    継続中
     

  • 数理材料学特論A

    早稲田大学  

    2019年04月
    -
    継続中
     

  • 変分法と解析力学A

    早稲田大学  

    2014年09月
    -
    継続中
     

  • ソリトンの数理A

    早稲田大学  

    2014年09月
    -
    継続中
     

  • 数学B1(微分積分)

    早稲田大学  

    2014年04月
    -
    継続中
     

  • Mathematics of Simulation

    早稲田大学  

    2014年09月
    -
    2020年02月
     

  • 数理モデル基礎A

    早稲田大学  

    2014年04月
    -
    2019年08月
     

▼全件表示

 

委員歴

  • 2017年06月
    -
    継続中

    日本応用数理学会  ICIAM Representative

  • 2017年06月
    -
    継続中

    日本応用数理学会  理事