耦合非线性薛定谔方程的平均离散梯度法  

Averaged Discrete Gradient Method for the Coupled Nonlinear Schr¨odinger Equations

作　　者：蒋朝龙[1] 黄荣芳[1] 孙建强[1] 

机构地区：[1]海南大学信息科学技术学院,海口570228

出　　处：《工程数学学报》2014年第5期707-718,共12页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(11161017);海南省自然科学基金(114003);海南省研究生创新科研课题(Hys201417);海南大学优秀研究生访学计划项目;海南大学研究生优秀学位论文培育计划~~

摘　　要：能量守恒格式对于准确地模拟微分方程的运动具有重要的意义.本文应用平均离散梯度法和辛算法求解耦合非线性薛定谔方程.数值结果表明平均离散梯度法能很好地模拟耦合非线性薛定谔方程在不同参数下孤立波的演化行为,并能精确地保持方程的离散能量.平均离散梯度法比相应的辛格式更好地保持方程的能量守恒.Energy preserving scheme is very important in simulating the behaviors of the d-ifferential equations. In this paper, we apply the average discrete gradient method and the symplectic method to solve the coupled nonlinear Schr＆#168;odinger equations. Numerical results show that the average discrete gradient method is able to simulate the solitary wave behaviors with different parameters very well, and also preserve the discrete energy of the coupled non-linear Schr＆#168;odinger equations exactly. The average discrete gradient method is better than the corresponding symplectic scheme in preserving the energy of the differential equation.

关 键 词：平均离散梯度格式 耦合非线性薛定谔方程 孤立波 

分 类 号：O241.5[理学—计算数学]