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

2012 Fiscal Year Final Research Report

• 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
• Keywords: 計算力学 / 可積分系

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
  • 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: 045206
  • 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
  • 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
• [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] 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] 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