广义Boussinesq方程的多辛方法

胡伟鹏; 邓子辰

广义Boussinesq方程的多辛方法

胡伟鹏¹,
邓子辰^1,2

1.
西北工业大学力学与土木建筑学院, 西安 710072;2.大连理工大学工业装备结构分析国家重点实验室, 辽宁大连 116023

基金项目: 国家自然科学基金资助项目(10572119;10772147;10632030);高校博士点基金资助项目(20070699028);陕西省自然科学基金资助项目(2006A07);大连理工大学工业装备结构分析国家重点实验室开放基金资助项目

详细信息

作者简介:
胡伟鹏(1977- ),男,湖北人,博士(E-mail:huweipeng@mail.nwpu.edu.cn);邓子辰(1964)),男,辽宁人,教授,博士,博士生导师(联系人.Tel:+86-29-88460403;E-mail:dweifan@nwpu.edu.cn).

中图分类号: O175.24
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出版历程
- 收稿日期: 2008-01-16
- 修回日期: 2008-05-09
- 刊出日期: 2008-07-15

Multi-Symplectic Method for Generalized Boussinesq Equation

HU Wei-peng¹,
DENG Zi-chen^1,2

1.
School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnincal University, Xi'an 710072, P. R. China;

摘要

摘要: 广义Boussinesq方程作为一类重要的非线性方程有着许多有趣的性质，基于Hamilton空间体系的多辛理论研究了广义Boussinesq方程的数值解法，构造了一种等价于多辛Box格式的新隐式多辛格式，该格式满足多辛守恒律、局部能量守恒律和局部动量守恒律．对广义Boussinesq方程孤子解的数值模拟结果表明,该多辛离散格式具有较好的长时间数值稳定性．
- 广义Boussinesq方程 /
- 多辛方法 /
- 孤子解 /
- 守恒律
Abstract: Generalized Boussinesq equation,representing a group of important nonlinear equations, possesses many interesting properties.The multi-symplectic formulations of which in Hamilton space were introduced.Then an implicit multi-symplectic scheme equivalent to the multi-symplectic Box scheme was constructed to solve the partial differential equations(PDEs) that were derived from the generalized Boussinesq equation.The numerical experiments on the soliton solutions of the generalized Boussinesq equation were also reported.Finally,the results of which show that the multi-symplectic method is an efficient algorithm with excellent long-time numerical behaviors for nonlinear partial differential equation.
- generalized Boussinesq equation /
- multi-symplectic method /
- soliton solution /
- conservation law

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参考文献(18)

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广义Boussinesq方程的多辛方法

作者简介:
胡伟鹏(1977- ),男,湖北人,博士(E-mail:huweipeng@mail.nwpu.edu.cn);邓子辰(1964)),男,辽宁人,教授,博士,博士生导师(联系人.Tel:+86-29-88460403;E-mail:dweifan@nwpu.edu.cn).

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Multi-Symplectic Method for Generalized Boussinesq Equation

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广义Boussinesq方程的多辛方法

作者简介: 胡伟鹏(1977- ),男,湖北人,博士(E-mail:huweipeng@mail.nwpu.edu.cn);邓子辰(1964)),男,辽宁人,教授,博士,博士生导师(联系人.Tel:+86-29-88460403;E-mail:dweifan@nwpu.edu.cn).

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出版历程

Multi-Symplectic Method for Generalized Boussinesq Equation

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出版历程

目录

作者简介:
胡伟鹏(1977- ),男,湖北人,博士(E-mail:huweipeng@mail.nwpu.edu.cn);邓子辰(1964)),男,辽宁人,教授,博士,博士生导师(联系人.Tel:+86-29-88460403;E-mail:dweifan@nwpu.edu.cn).