| 立方非线性薛定谔方程的新多级包络周期解 |
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| 引用本文： | 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].量子电子学报,2012,29(3):269-278. |
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| 作者姓名： | 肖亚峰 薛海丽 张鸿庆 |
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| 作者单位： | 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 |
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| 基金项目： | 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 |
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| 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。
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| 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 |
| 收稿时间： | 2011/5/9 |
| 修稿时间： | 2012-05-09 |
New multi-order envelope periodic solutions to cubic nonlinear Schrodinger equation |
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| XIAO Ya-feng
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XUE Hai-li
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ZHANG Hong-qing.New multi-order envelope periodic solutions to cubic nonlinear Schrodinger equation[J].Chinese Journal of Quantum Electronics,2012,29(3):269-278. |
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| Authors: | XIAO Ya-feng XUE Hai-li ZHANG Hong-qing |
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| Affiliation: | 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 |
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| 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 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. |
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| Keywords: | nonlinear equation multi-order envelope periodic solutions perturbation method Lame equation Jacobi elliptic function cubic nonlinear Schrodinger equation |
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