Camassa-Holm方程的多辛Fourier拟谱格式

Multi-Symplectic Fourier Pseudo-Spectral Scheme of the Camassa-Holm Equation

对满足周期边界条件的Camassa-Holm(CH)方程,基于其多辛方程组的形式,空间方向用Fourier拟谱方法,时间方向用中点隐式辛格式进行离散,得到了CH方程的多辛Fourier拟谱格式及其离散的多辛守恒律.数值实验验证了所构造格式的有效性与长期数值稳定性.

The Camassa-Holm equation（CHE） with periodic boundary condition is considered in this paper. Based on its multi-symplectic formulation, a multi-symplectic Fourier pseudo-spectral scheme for the CHE is constructed by using Fourier pseudo-spectral method in space direction and midpoint implicit symplectic scheme in time direction. Its discrete multi-symplectic conservation law is also obtained. Numerical experiments show that the scheme constructed in this paper is effective and has excellent long time numerical behavior.