New moving mesh numerical scheme based on the theory of integrable systems and its applications

• Project/Area Number: 22656026
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Single-year Grants
• Research Field: Engineering fundamentals
• Research Institution: Kobe University
• Principal Investigator: OHTA Yasuhiro 神戸大学, 大学院・理学研究科, 教授 (10213745)
• Project Period (FY): 2010 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥2,160,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥360,000); Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2010: ¥600,000 (Direct Cost: ¥600,000)
• Keywords: 計算力学 / 可積分系 / 数値シミュレーション / 自動適応ムービングメッシュ / ホドグラフ変換 / ソリトン / Camassa-Holm方程式

Research Abstract

By applying the theory of discrete nonlinear integrable systems, self-adaptive moving mesh schemes are constructed for various equations, in which the grid points are driven and adapted automatically by solution so that the results become accurate and stable.

Research Products

• [Journal Article] On the γ -Functions of the ReducedOstrovsky Equation and the A_2^(2) Two-Dimensional Toda System (2012)
  • Author(s): B-F、Feng, K. Maruno and Y.ohta
  • Journal Title: J. Phys. A:Math. Teor Volume: 45 Pages: 355203-355203
  • Peer Reviewed
• [Journal Article] General High-Order Rougue Waves and Their Dynamics in the Nonlinear SchrOdinger Equation (2012)
  • Author(s): Y.ohta and J.Yang
  • Journal Title: Proc. R. soc.A Volume: 468 Pages: 17165-1740
  • Peer Reviewed
• [Journal Article] Explicit Solution to the Semi-Discrete Modified Kdv Equation and Motion of Discrete Plane Curves (2012)
  • Author(s): J. Inoguchi, K. Kajiwara, N, Matsuura and Y.Ohta
  • Journal Title: J. Phys. A : Math. Teor Volume: 45 Pages: 45206-45206
  • Peer Reviewed
• [Journal Article] Explicit solutions to the semi-discrete modified KdV equation and motion of discrete plane curves (2012)
  • Author(s): J. Inoguchi
  • Journal Title: J. Phys. A: Math. Theor. Volume: 45 Pages: 45206-45206
  • Peer Reviewed
• [Journal Article] General high-order rogue waves and their dynamics in the nonlinear Schr\"odinger equation (2012)
  • Author(s): Y. Ohta
  • Journal Title: Proc. R. Soc. A Volume: 468 Pages: 1716-1740
  • Peer Reviewed
• [Journal Article] On the $\tau$-functions of the reduced Ostrovsky equation and the $A_2^{(2)}$ two-dimensional Toda system (2012)
  • Author(s): B.-F. Feng
  • Journal Title: J. Phys. A: Math. Theor. Volume: 45 Pages: 355203-355203
  • Peer Reviewed
• [Journal Article] Genaral N-Dark-Dark Solutions in the Coupled Non-linear SchrOdinger Equations (2011)
  • Author(s): Y. ohta, D, s.Wang and J.Yang
  • Journal Title: stud. Appl.Math Volume: 127 Pages: 345-371
  • Peer Reviewed
• [Journal Article] Discrete Integrable Systems and Hodgreph Transformations Arising from Motions of Discrete Plane Curves (2011)
  • Author(s): B.-F. Feng, J. Inoguchi, K. Kajiwara, K. Maruno and Y. ohta
  • Journal Title: J. Phys A: Math. Theor Volume: 44 Pages: 395201-395201
  • Peer Reviewed
• [Journal Article] Discrete integrable systems and hodograph transformations arising from motions of discrete plane curves (2011)
  • Author(s): B.-F.Feng, et al
  • Journal Title: J.Phys.A : Math.Theor. Volume: 44 Pages: 395201-395201
  • Peer Reviewed
• [Journal Article] General N-dark-dark solitons in the coupled nonlinear Schrodinger equations (2011)
  • Author(s): Y.Ohta, et al
  • Journal Title: Stud.Appl.Math. Volume: 127 Pages: 345-371
  • Peer Reviewed
• [Journal Article] A self-Adaptive Moving Mesh Method for the Camassa-Holm Equation (2010)
  • Author(s): B.-F. Feng, K. Maruno and Y.ohta
  • Journal Title: J. Compuut. Apple Mash Volume: 235 Pages: 229-243
  • Peer Reviewed
• [Journal Article] A Self-Adaptive Moving Mesh Method for the Camassa-Holm Equation (2010)
  • Author(s): B.F.Feng, et al.
  • Journal Title: J.Comput.Appl.Math. Volume: 235 Pages: 229-243
  • Peer Reviewed
• [Presentation] BKP with 2-reducation (2013)
  • Author(s): Y. ohta
  • Organizer: Chine-Japan Joint Workshop on Integrable Systems 2013
  • Place of Presentation: Kyoto, Japan
  • Year and Date: 2013-03-17
• [Presentation] BKP with 2-reduction (2013)
  • Author(s): Y. Ohta
  • Organizer: China-Japan Joint Workshop on Integrable Systems 2013
  • Place of Presentation: Kyoto, Japan
  • Invited
• [Presentation] Discretization of solution equations derived through hodograph transformation (2012)
  • Author(s): Y.ohta
  • Organizer: 2012 Tokyo Workshop on Structure-Preserving Methods
  • Place of Presentation: Tokyo, Japan
  • Year and Date: 2012-01-16
• [Presentation] Discretization of soliton equations derived through hodograph transformation (2012)
  • Author(s): Y.Ohta
  • Organizer: 2012 Tokyo Workshop on Structure-Preserving Methods
  • Place of Presentation: 東京大学(東京都)
  • Year and Date: 2012-01-16
• [Presentation] 可積分系数理の進化 (2011)
  • Author(s): 太田泰広
  • Organizer: 差分ソリトン方程式の話題RIMS研究集会
  • Place of Presentation: 京都、日本
  • Year and Date: 2011-08-18
• [Presentation] Discretization of integrable systems with hodograph transformation (2010)
  • Author(s): Y. ohta
  • Organizer: Satelite conference of the ICM 2010:Integrable Systems and Geometory
  • Place of Presentation: Puducherry, India
  • Year and Date: 2010-08-17
• [Presentation] Discretization of integrable systems with hodograph transformation (2010)
  • Author(s): Y.Ohta
  • Organizer: Satellite conference of the ICM 2010 : Integrable Systems and Geometry
  • Place of Presentation: Puducherry, India(招待講演)
  • Year and Date: 2010-08-17