非线性Schrödinger方程几类孤立子解:局部间断Petrov-Galerkin方法  

Several Kinds of Soliton Solution of Nonlinear Schrödinger Equation:Local Discontinuous Petrov⁃Galerkin Method

作　　者：赵国忠[1] 蔚喜军[2] 董自明 郭虹平 郭鹏云[1] 李姝敏[1] ZHAO Guozhong;YU Xijun;DONG Ziming;GUO Hongping;GUO Pengyun;LI Shumin(Faculty of Mathematics,Baotou Teachers’College,Baotou,Inner Mongolia 014030,China;Laboratory of Computational Physics,Institute of Applied Physics and Computational Mathematics,Beijing 100088,China)

机构地区：[1]包头师范学院数学科学学院,内蒙古包头014030 [2]北京应用物理与计算数学研究所计算物理实验室,北京100088

出　　处：《计算物理》2022年第6期641-650,共10页Chinese Journal of Computational Physics

基　　金：National Natural Science Foundation of China(11761054,12071046,11261035);the Natural Science Foundation of Inner Mongolia Autonomous Region,China(2021MS01001,2015MS0108,2012MS0102);the Science Research Foundation of Institute of Higher Education of Inner Mongolia Autonomous Region,China(NJZY19186,NJZZ12198)

摘　　要：构造一类求解非线性薛定谔方程的局部间断Petrov-Galerkin方法。利用构造的方法模拟几种类型的孤立子并讨论与孤立子密切相关的一些现象,包括孤立子的传播与碰撞,动孤立子和驻孤立子的生成,N孤立子的有界态。该方法可以模拟孤立子相关现象中一些复杂结构。数值实验表明该方法具有高阶精度且可以达到最优收敛阶。局部间断Petrov-Galerkin方法的计算效率与局部间断Galerkin方法相当,但计算公式简单。A local discontinuous Petrov⁃Galerkin method is developed for nonlinear Schrödinger equations.Several kinds of solitons are simulated and related phenomena are discussed,such as the soliton propagation and collision,birth of solitons including standing soliton and mobile soliton,the bound state of N solitons.The algorithm simulates some narrow structures in soliton related phenomenon.Numerical examples show that the algorithm has high accuracy and can reach the optimal convergence order.Compared with local discontinuous Galerkin method,the local discontinuous Petrov⁃Galerkin method has high computational efficiency and simple computational formula.

关 键 词：局部间断Petrov-Galerkin方法 非线性薛定谔方程 孤立子 N孤立子的有界态 

分 类 号：O241.82[理学—计算数学]