立方非线性薛定谔方程的新多级包络周期解

J4 ›› 2012, Vol. 29 ›› Issue (3): 269-278.

立方非线性薛定谔方程的新多级包络周期解

肖亚峰¹, 薛海丽², 张鸿庆³

1中北大学数学系，山西太原 030051；
2 中北大学软件学院，山西太原 030051
3 大连理工大学数学科学学院，辽宁大连 116024

收稿日期:2011-05-09 修回日期:2012-05-09 出版日期:2012-05-28 发布日期:2012-05-22
通讯作者: 肖亚峰(1976-)讲师,博士生,主要从事符号计算与非线性物理研究. E-mail:yafengxiao@126.com
基金资助:
国家重点基础研究专项基金(2004CB318000), 国家自然科学基金青年基金(10901145),中北大学校基金资助项目

New multi-order envelope periodic solutions to the cubic nonlinear Schrodinger equation

XIAO Ya-feng ¹, XUE Hai-li ², ZHANG Hong-qing³

1 Department of Mathematics, North University of China, Taiyuan 030051, China;
2 Software School, North University of China, Taiyuan 030051, China;
3 School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China

Received:2011-05-09 Revised:2012-05-09 Published:2012-05-28 Online:2012-05-22

摘要/Abstract

摘要：

基于Lame方程和新的Lame函数，应用摄动方法和Jacobi椭圆函数展开法求解立方非线性薛定谔方程，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Lamé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。

关键词: 非线性方程, 多级包络周期解, 摄动方法, Lame方程, Jacobi椭圆函数, 立方非线性薛定谔方程

Abstract:

Based on the Lame equation and Lame functions, the perturbation method and Jacobi elliptic function expansion method are applied to construct the multi-order exact solutions to the cubic nonlinear Schrodinger equation. Some new multi-order envelope periodic solutions are 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 equation are explicitly obtained with the aid of symbolic computation.

Key words: nonlinear equation, multi-order envelope periodic solutions, perturbation method, Lame equation, Jacobi elliptic function, cubic nonlinear Schrodinger equation

中图分类号:

O175.2

肖亚峰薛海丽张鸿庆. 立方非线性薛定谔方程的新多级包络周期解[J]. J4, 2012, 29(3): 269-278.

XIAO Ya-feng, XUE Hai-li, ZHANG Hong-qing. New multi-order envelope periodic solutions to the cubic nonlinear Schrodinger equation[J]. J4, 2012, 29(3): 269-278.

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