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
Zhiber-Shabat方程的多辛几何和多辛隐式格式研究
Multi-Symplectic Geometry and Explicit Multi-symplectic Method for Solving Zhiber-Shabat Equation
投稿时间:2014-09-23  最后修改时间:2015-03-04
DOI:10.3770/j.issn:2095-2651.2015.05.008
中文关键词:  Zhiber-Shabat方程  多辛理论  Fourier拟谱方法  局部守恒律
英文关键词:the Zhiber-Shabat equation  multi-symplectic theory  Fourier pseudospectral method  local conservation laws
基金项目:
作者单位
王俊杰 普洱学院数学与统计学院, 云南 普洱 665000 
李胜平 普洱学院数学与统计学院, 云南 普洱 665000 
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中文摘要:
      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.
英文摘要:
      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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