| Zhiber-Shabat方程的多辛几何和多辛隐式格式研究 |
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| 引用本文： | 王俊杰,李胜平. Zhiber-Shabat方程的多辛几何和多辛隐式格式研究[J]. 数学研究及应用, 2015, 35(5): 551-560 |
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| 作者姓名： | 王俊杰 李胜平 |
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| 作者单位： | 普洱学院数学与统计学院, 云南 普洱 665000;普洱学院数学与统计学院, 云南 普洱 665000 |
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| 摘 要： | Zhiber-Shabat方程,描述许多重要的物理现象,是一类重要的非线性方程,有着许多广泛的应用前景.本文给出Zhiber-Shabat方程的多辛几何结构和多辛Fourier拟谱方法.数值算例结果表明多辛离散格式具有较好的长时间的数值稳定性.
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| 关 键 词： | Zhiber-Shabat方程 多辛理论 Fourier拟谱方法 局部守恒律 |
| 收稿时间： | 2014-09-23 |
| 修稿时间： | 2015-03-04 |
Multi-Symplectic Geometry and Explicit Multi-symplectic Method for Solving Zhiber-Shabat Equation |
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| Junjie WANG and Shengping LI. Multi-Symplectic Geometry and Explicit Multi-symplectic Method for Solving Zhiber-Shabat Equation[J]. Journal of Mathematical Research with Applications, 2015, 35(5): 551-560 |
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| Authors: | Junjie WANG and Shengping LI |
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| Affiliation: | Mathematics and Statistical Institute, Pu Er University, Yunnan 665000, P. R. China;Mathematics and Statistical Institute, Pu Er University, Yunnan 665000, P. R. China |
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| Abstract: | In the paper, we derive a multi-symplectic Fourier pseudospectral method for Zhiber-Shabat equation. The Zhiber-Shabat equation, which describes many important physical phenomena, has been investigated widely in last several decades. The multi-symplectic geometry and multi-symplectic Fourier pseudospectral method for the Zhiber-Shabat equation is presented. The numerical experiments are given, showing that the multi-symplectic Fourier pseudospectral method is an efficient algorithm with excellent long-time numerical behaviors. |
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| Keywords: | the Zhiber-Shabat equation multi-symplectic theory Fourier pseudospectral method local conservation laws |
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