带色散项的高阶非线性Schrdinger方程的精确解  

Exact wave solutions for the higher-order nonlinear Schrdinger equation with a dispersion term

作　　者：曹瑞[1] 

机构地区：[1]菏泽学院数学系,山东菏泽274000

出　　处：《纯粹数学与应用数学》2012年第1期92-98,共7页Pure and Applied Mathematics

基　　金：菏泽学院科学研究基金(XY07SX01)

摘　　要：对一类带色散项的高阶非线性Schrdinger方程的精确解进行研究.通过行波约化,将一类带色散项的高阶非线性Schrdinger方程化为一个高阶非线性常微分方程.再借助于计算机代数系统Mathematica通过构造非线性常微分方程的精确解,成功获得了一系列含有多个参数的包络型精确解,当精确解中参数取特殊值时可以得到两种新型的复合孤子解.并讨论了这两种孤子解存在的参数条件.Exact solutions of the higher-order nonlinear SchrSdinger equation with a dispersion term are studied. By traveling wave reduction, the higher-order nonlinear Schr＇Sdinger equation are transformed into nonlinear ordinary differential equation, and then by constructing a series of exact solutions of nonlinear ordinary differential equation, many.envelope type exact wave solutions containing multiple parameters are obtained for the higher-order nonlinear Schrodinger equation with the aid of computer algebraic system Mathematica. when parameters are taken specific values, two new kind of soliton solution are obtained. And the conditions of the existence of soliton solution are discussed.

关 键 词：高阶非线性Schrdinger方程 精确解 孤立波解 

分 类 号：O175.29[理学—数学]