复修正KdV方程的多辛整体保能量方法

Global Energy-Preserving Method for the Complex Modified KdV Equations

基于二阶平均向量场方法和拟谱方法,构造了具有多辛结构的复修正Kd V方程新的数值格式,证明了该格式能保方程离散的整体能量守恒特性,并利用该格式在不同初始条件下数值模拟复修正Kd V方程孤立波的演化行为及分析格式的保能量守恒特性.数值实验表明:新的数值格式具有精确保持离散整体能量守恒的性质.

A new numerical scheme for the multi-symplectic complex modified Kd V equation is constructed by the second order average vector field method and pseudo-spectral method. The corresponding discrete global energy conservation property of the new schemes is proved. The new schemes are applied to simulate the solitary wave evolution behaviors of the complex modified Kd V equation with different initial conditions. The preserving energy conservation property is analyzed. Numerical results show that the new scheme can preserve the discrete global energy conservation property.