广义变系数(3+1)-维非线性薛定谔方程的有限对称群解

J4 ›› 2016, Vol. 33 ›› Issue (3): 263-278.

广义变系数(3+1)-维非线性薛定谔方程的有限对称群解

郝鑫星¹,李彪²

宁波大学理学院，浙江宁波 315211

收稿日期:2015-08-06 修回日期:2015-11-14 出版日期:2016-05-28 发布日期:2016-05-27

Finite symmetry group solutions to a generalized variable coefficients (3+1)-dimensional nonlinear Schr\"{o}ding equation

Received:2015-08-06 Revised:2015-11-14 Published:2016-05-28 Online:2016-05-27

摘要/Abstract

摘要： 基于推广的对称群方法和符号计算，研究了变系数非线性薛定谔方程的有限对称群解。我们构造了标准的(3+1)-维非线性薛定谔方程和带色散项、非线性项和增益或损耗项的(3+1)-维非线性薛定谔方程的对称变换。利用该变换，我们从标准的(3+1)-维非线性薛定谔方程中得到了(3+1)-维变系数非线性薛定谔方程丰富的精确解。

关键词: 符号计算

Abstract: In this paper, on the basis of the extending symmetry group approach and symbolic computation, some finite symmetry group solutions of the nonlinear Schr\"{o}dinger (NLS) equations with various variable coefficients are investigated. We construct some symmetry transformations between the standard (3+1)-dimensional NLS equation and (3+1)-dimensional NLS equations with distributed dispersion,nonlinearity and gain or loss. By using these symmetry transformations, rich exact solutions of some (3+1)-dimensional variable coefficients NLS equations are obtained from the standard (3+1)-dimensional NLS equation.

Key words: symbolic

中图分类号:

O175.29

郝鑫星李彪. 广义变系数(3+1)-维非线性薛定谔方程的有限对称群解[J]. J4, 2016, 33(3): 263-278.

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