含五次非线性项的Schrödinger方程的多辛算法  

Multi-symplectic Algorithm for Schrödinger Equation with Quintic Nonlinear Term

作　　者：徐金平[1] 陈特清[2] XU Jinping;CHEN Teqing(School of Information Management, Minnan University of Science and Technology, Shishi, Fujian 362700, China;School of Education, Minnan University of Science and Technology, Shishi, Fujian 362700, China)

机构地区：[1]闽南理工学院信息管理学院,福建石狮362700 [2]闽南理工学院教育学院,福建石狮362700

出　　处：《平顶山学院学报》2022年第2期1-4,共4页Journal of Pingdingshan University

基　　金：福建省中青年教师教育科研资助项目(JAT200766)。

摘　　要：通过引入正则变量得到方程的多辛哈密尔顿系统的形式,然后在时空方向均用辛Runge-Kutta方法离散,构造了方程的多辛Preissman格式,最后用数值实验验证了该格式具有长时间的数值稳定性.This study obtains the form of multi-symplectic Hamiltonian system of the equation by introducing regular variables,then discretizes the spatial and temporal directions with symplectic Runge-Kutta method,and constructs the multi-symplectic Preissman scheme.Finally,numerical experiments show that the scheme has long-term numerical stability.

关 键 词：非线性Schrödinger方程 多辛Preissman格式 多辛守恒律 局部能量守恒律 局部动量守恒律 

分 类 号：O241.82[理学—计算数学]