非线性与立方非线性Schr dinger方程的多级准确解  

The Multi-order Exact Solutions for the Nonlinear Schr dinger Equation and Cubic Nonlinear Schr dinger Equation

作　　者：钱天虹[1] 刘中飞[2] 韩家骅[2] 

机构地区：[1]安徽中医学院药学系物理实验室安徽合肥,230031 [2]安徽大学物理系,安徽合肥230039

出　　处：《安徽教育学院学报》2005年第3期12-14,共3页Journal of Anhui Institute of Education

基　　金：安徽省科技厅年度重点项目(01041188);安徽省教育厅自然科学基金(2000j1002)

摘　　要：本文利用摄动法对非线性与立方非线性Schr dinger方程作展开。应用Jacobi椭圆函数展开法求得了零级近似方程的准确解,并在Lamé方程和Lamé函数的基础上分别求得一级近似方程和二级近似方程的准确解。这样,就求得了非线性与立方非线性Schr dinger方程的多级准确解。The perturbation method is applied to the multi-order exact solutions of the nonliner Schrodinger equation and cubic nonlinear Schroedinger equation nonlinear evolution. The exact solutions to the zerothorder equation can be derived by Jacobi elliptic function expansion method,and then the first-order and the second-order equations can be solved by using Lamé equation and lame functions. Thus,the multi-order exact solutions are obtained to the nonlinear Schrodiner equation and cubic nonlinear Schrodinger equation.

关 键 词：非线性与立方非线性Schroedinger方程 摄动法 Lamé函数 JACOBI椭圆函数 多级准确解 

分 类 号：O175.2[理学—数学]