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

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

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.