(2+1)维MKdV方程的Darboux变换及其孤子解

吉林大学学报(理学版)

(2+1)维MKdV方程的Darboux变换及其孤子解

黄坤¹, 吕悦²

1. 华北水利水电大学数学与信息科学学院, 郑州 450011; 2. 吉林大学数学学院, 长春 130012

收稿日期:2012-07-03 出版日期:2013-07-26 发布日期:2013-08-06
通讯作者: 黄坤 E-mail:huangkun@ncwu.edu.cn

Darboux Transformations for (2+1)DimensionalMKdV Equation and Its Soliton Solution

HUANG Kun¹, LV Yue²

1. College of Mathematics and Information Science, North China University of Water Resources andElectric Power, Zhengzhou 450011, China; 2. College of Mathematics, Jilin University, Changchun 130012, China

Received:2012-07-03 Online:2013-07-26 Published:2013-08-06
Contact: HUANG Kun E-mail:huangkun@ncwu.edu.cn

摘要/Abstract

摘要：

利用Darboux变换求解(2+1)维MKdV方程的孤子解. 先从广义MKdV方程的谱问题出发, 推导出(2+1)维MKdV方程及其对应的Lax对；再借助零曲率方程构造(2+1)维MKdV方程3种不同的Darboux变换, 并讨论了3种Darboux变换间的关系.

关键词: MKdV方程, Darboux变换, 孤子解

Abstract:

Soliton solutions of (2+1) dimensional MKdV equation were obtained via Darboux transformation. Based on spectral problems of the generalized MKdV equation, a (2+1) dimensional MKdV equation and its Lax pairs were derived . With the help of zero curvature equation, three different Darbouxtransformations (DTs) of the (2+1) dimensional MKdV equations were constructed. Then, relations among three Darboux transformations were discussed. As an example of application of DT, soliton solutions of (2+1) dimensional MKdV equation were given and various collision graphics were discussed.

Key words: MKdV equation, Darboux transformation, soliton solution

中图分类号:

O175.29

黄坤, 吕悦. (2+1)维MKdV方程的Darboux变换及其孤子解[J]. 吉林大学学报(理学版), 2013, 51(04): 573-579.

HUANG Kun1, LV Yue2. Darboux Transformations for (2+1)DimensionalMKdV Equation and Its Soliton Solution[J]. Journal of Jilin University Science Edition, 2013, 51(04): 573-579.

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