KdV 方程和mKdV 方程的新奇异解

刘正荣 唐昊

doi:1000-565X(2012)10-0096-06

华南理工大学学报(自然科学版) >

2012 , Vol. 40 >Issue 10: 96 - 101

DOI: https://doi.org/1000-565X(2012)10-0096-06

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KdV 方程和mKdV 方程的新奇异解

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华南理工大学数学系，广东广州 510640

刘正荣(1955-) ，男，教授，博士生导师，主要从事非线性动力系统研究．

收稿日期: 2012-07-10

网络出版日期: 2012-09-01

基金资助

国家自然科学基金资助项目( 11171115)

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New Singular Solutions of KdV and mKdV Equations

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Department of Mathematics,South China University of Technology,Guangzhou 510640,Guangdong,China

Liu Zheng-rong ( born in 1955) ，male，professor，Ph．D．tutor，mainly reasearches on nonlinear dynamic systems．

Received date: 2012-07-10

Online published: 2012-09-01

Supported by

Supported by the National Natural Science Foundation of China ( 11171115)

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摘要

研究了著名的KdV 方程和mKdV 方程的奇异解．首先，建立了与这两个方程相应的平面行波系统．然后，利用行波系统的一些特殊轨道，导出了新奇异解．最后，通过mKdV 方程的奇异解以及Miura 变换，获得了KdV 方程其它的新奇异解．

关键词： KdV 方程; mKdV 方程; 奇异解; Miura 变换

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刘正荣唐昊 . KdV 方程和mKdV 方程的新奇异解[J]. 华南理工大学学报(自然科学版), 2012 , 40(10) : 96 -101 . DOI: 1000-565X(2012)10-0096-06

Abstract

This paper deals with the singular solutions of the famous KdV and mKdV equations. In the investigation,first,the corresponding planar systems of these equations are established. Then,through some special orbits of the corresponding planar systems,some new singular solutions of these equations are obtained. Finally,by employing the singular solutions of the mKdV equation and the Miura transformations,other singular solutions of the KdV equation are presented.

Key words： KdV equation; mKdV equation; singular solution; Miura transformation

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