非线性薛定谔方程的新多级包络周期解  

New Multi-Order Envelope Periodic Solutions to the Nonlinear Schrodinger Equation

作　　者：肖亚峰[1] 薛海丽[2] 

机构地区：[1]中北大学理学院，山西 太原 030051 [2]中北大学软件学院，山西 太原 030051

出　　处：《中北大学学报（自然科学版）》2013年第1期1-4,16,共5页Journal of North University of China(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10901145);中北大学校基金资助项目

摘　　要：基于Lam·方程和新的Lam·函数,应用摄动方法和Jacobi椭圆函数展开法研究非线性薛定谔方程,获得多种新的多级准确解.这些解对应着不同的形式的包络周期解.这些解在极限条件下可以退化为各种形式的包络孤波解.这表明利用Jacobi椭圆函数和Lam·方程,在符号计算的帮助下,可获得若干非线性发展方程的多级渐进周期解.Based on the Lame equation and Lame functions,the perturbation method and Jacobi elliptic function expansion method were applied to construct the multi-order exact solutions to the nonlinear Schrdinger equation.Some new multi-order envelope periodic solutions were found among the nonlinear evolution equation.These multi-order envelope periodic solutions correspond to different periodic solutions,which can degenerate into the different envelope solitary solutions.It is shown that some multi-order asymptotic periodic solutions to some nonlinear evolution equations in term of Jacobi elliptic functions and Lame equations are explicitly obtained with the aid of symbolic computation.

关 键 词：非线性方程 多级包络周期解 摄动方法 Lam·方程 JACOBI椭圆函数 非线性薛定谔方程 

分 类 号：O175.2[理学—数学]