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

基于可积系统理论的新型动网格数值格式及其应用

• 批准号: 22656026
• 负责人: OHTA Yasuhiro
• 金额: $ 1.38万
• 依托单位: Kobe University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Challenging Exploratory Research
• 财政年份: 2010
• 资助国家: 日本
• 起止时间: 2010 至 2012
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22656026/
• 关键词: 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

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.

应用离散非线性可积系统理论，构造了各种方程的自适应移动网格格式，通过求解自动驱动和调整网格点，使结果具有较高的精度和稳定性。

项目成果

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

• DOI: 10.1016/j.cam.2010.05.044
• 发表时间: 2009-05
• 期刊: J. Comput. Appl. Math.
• 作者: B. Feng;K. Maruno;Y. Ohta

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

• DOI: 10.1088/1751-8113/44/39/395201
• 发表时间: 2011-07
• 期刊: Journal of Physics A: Mathematical and Theoretical
• 作者: B. Feng;J. Inoguchi;K. Kajiwara;K. Maruno;Y. Ohta

On the $\tau$-functions of the reduced Ostrovsky equation and the $A_2^{(2)}$ two-dimensional Toda system

关于简化奥斯特洛夫斯基方程和$A_2^{(2)}$二维Toda系统的$ au$函数

• 发表时间: 2012
• 期刊: J. Phys. A: Math. Theor.
• 作者: S. Kitazaki;K. Koga;M. Shiratani;N. Hayashi;萩行正憲;濱田慎平;白谷正治;K. Takano et al.;武田征士;濱田慎平;萩行正憲;萩行正憲;Y. Ohta;北崎訓,古閑一憲,白谷正治,林信哉,白谷正治;萩行正憲;濱田慎平;B.-F. Feng
• 通讯作者: B.-F. Feng

Discrete Integrable Systems and Hodgreph Transformations Arising from Motions of Discrete Plane Curves

离散可积系统和离散平面曲线运动引起的Hodgreph变换

• 发表时间: 2011
• 期刊: J. Phys A: Math. Theor
• 作者: B.-F. Feng;J. Inoguchi;K. Kajiwara;K. Maruno and Y. ohta
• 通讯作者: K. Maruno and Y. ohta

Genaral N-Dark-Dark Solutions in the Coupled Non-linear SchrOdinger Equations

耦合非线性薛定谔方程中的一般N-Dark-Dark解

• 发表时间: 2011
• 期刊: stud. Appl.Math
• 作者: Y. ohta;D;s.Wang and J.Yang
• 通讯作者: s.Wang and J.Yang