立方非线性薛定谔方程的新多级包络周期解  

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

作　　者：肖亚峰[1] 薛海丽[2] 张鸿庆[3] 

机构地区：[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

出　　处：《量子电子学报》2012年第3期269-278,共10页Chinese Journal of Quantum Electronics

基　　金：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

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了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Lame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 are applied to construct the multi-order exact solutions to the cubic nonlinear SchrSdinger equation. Some new multi-order envelope periodic solutions are found among the nonlinear evolution equations. 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： tion： Jacobi nonlinear equation; multi-order envelope periodic solutions; perturbation method; Lame equaelliptic function; cubic nonlinear SchrSdinger equation

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 

分 类 号：O175.2[理学—数学]