二维阻尼非线性sine-Gordon方程的共形多辛Fourier拟谱格式  

A conformal multi-symplectic Fourier pseudo-spectral scheme for two dimensional nonlinear damped sine-Gordon equation

作　　者：王杰 蒋朝龙 WANG Jie;JIANG Chaolong(School of Mathematics and Statistics,Yunnan University of Finance and Economics,Kunming 650221,China)

机构地区：[1]云南财经大学统计与数学学院,云南昆明650221

出　　处：《纯粹数学与应用数学》2023年第2期214-232,共19页Pure and Applied Mathematics

基　　金：国家自然科学基金(12261097);云南省教育厅科学研究基金(2022J0907);云南省基础研究计划项目(202101AT070208,202101AS070044).

摘　　要：为二维阻尼非线性sine-Gordon方程构造了一个新的共形多辛Fourier拟谱格式.基于原系统的共形多辛哈密尔顿形式,首先在时间和空间方向上分别用辛中点和Fourier拟谱方法进行离散,得到一个全离散格式.随后证明了构造的格式保持离散的共形多辛守恒律.最后数值实验验证了格式的有效性.In this paper,a conformal multi-symplectic Fourier pseudo-spectral scheme is proposed for two dimensional nonlinear damped sine-Gordon equation.Based on the conformal multi-symplectic formulation of the original equation,the fully discrete scheme is obtained by using the symplectic middle point scheme and Fourier pseudo-spectral method to the formulation in time and space,respectively.Then,it is proven that the proposed scheme can preserve the conformal multi-symplectic conservation law.Finally,numerical experiments are addressed to demonstrate the efficiency of the proposed scheme.

关 键 词：阻尼sine-Gordon方程 共形多辛格式 FOURIER拟谱方法 孤立子 

分 类 号：O241.8[理学—计算数学]