高阶非线性薛定谔方程的离散梯度法  

Dispersed Gradient Method of High Order Nonlinear Schrdinger Equation

作　　者：骆思宇[1] 蒋朝龙[1] 孙建强[1] 

机构地区：[1]海南大学信息科学技术学院,海南海口570228

出　　处：《海南大学学报（自然科学版）》2013年第2期112-118,共7页Natural Science Journal of Hainan University

基　　金：国家自然科学基金项目(11071251);海南省自然科学基金项目(110002);海南省自然科学基金项目(113001);海南大学科研启动基金项目(kyqd1053)

摘　　要：提出了一种新的离散梯度法求解高阶非线性薛定谔方程.首先利用离散梯度法离散高阶非线性薛定谔方程,得到高阶非线性薛定谔方程的离散梯度格式,然后利用高阶非线性薛定谔方程的离散梯度格式和相应的辛格式,在不同饱和非线性效应和不同振辐下对孤立子进行数值模拟.数值结果表明,离散梯度格式能很好地模拟高阶非线性薛定谔方程中孤立子行为,比辛格式更好地保持Hamilton系统的能量.In the report, a new dispersed gradient method was proposed for solving the high order nonlinear Schrodinger Equation. Firstly, the dispersed gradient method was used to discrete the high order nonlinear Schrodinger Equation and the dispersed gradient scheme of the high order nonlinear Schrodinger Equation was obtained. Secondly, the discrete gradient scheme and the corresponding symplectic scheme of the high order nonlinear Schrodinger Equation with the different saturated nonlinear effects and the different amplitudes were used to simulate the soliton behaviors. The results indicated that the dispersed gradient scheme can simulate the solitons behaviors of the high order nonlinear Schrodinger equation very well and preserve the energy conservation of the Hamiltonian system better than the symplectic scheme.

关 键 词：高阶非线性薛定谔方程 离散梯度法 孤立子 

分 类 号：O431.2[机械工程—光学工程] O241.82[理学—光学]