构造非线性演化方程精确解的一个新方法

J4 ›› 2012, Vol. 29 ›› Issue (3): 279-285.

构造非线性演化方程精确解的一个新方法

邱春刁明军徐兰兰岳书波赵静

四川大学水力学与山区河流开发保护国家重点实验室, 四川成都 610065

收稿日期:2011-06-07 修回日期:2011-08-06 出版日期:2012-05-28 发布日期:2012-05-22
通讯作者: 刁明军 (1968- ), 四川成都人，教授，博士生导师，主要从事工程水力学的科研与教学工作。 E-mail:diaomingjun@scu.edu.cn
作者简介:邱春 (1976- )江苏徐州人, 博士生，研究方向为非线性物理及工程水力学。Email:qiu3216@163.com

A new algebra method for constructing exact solutions of nonlinear evolution equations

QIU Chun, DIAO Ming-jun, XU Lan-lan, YUE Shu-bo, ZHAO Jing

State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu 610065, China

Received:2011-06-07 Revised:2011-08-06 Published:2012-05-28 Online:2012-05-22

摘要/Abstract

摘要：

基于辅助方程提出一种求解非线性演化方程的一个新方法，该方法简单易行且具有一定的普适性，根据不同的参数可给出各种形式的精确解，从而有助于探索非线性方程的新解及其性质。并以mkdv方程为例，得到了其多组精确解，包括Jacobi椭圆函数解及Weierstrass椭圆函数解等，除涵盖了以往结果，还给出一些新解。

关键词: 非线性方程, 精确解, 辅助方程, mkdv方程

Abstract:

A new algebra method for constructing exact solutions of nonlinear evolution equations is proposed based on the auxiliary equation; the method is simple and universal. It can give various types of exact solutions according to different parameters, which will be helpful to seek more new exact solutions and explore properties of nonlinear evolution equations. As an application, many kinds of explicit solutions including Jacobi and Weierstrass elliptic function solutions etc are obtained, some of which are new.

Key words: nonlinear equation, exact solution, auxiliary equation, mkdv equation

中图分类号:

O175

邱春刁明军徐兰兰岳书波赵静. 构造非线性演化方程精确解的一个新方法[J]. J4, 2012, 29(3): 279-285.

QIU Chun, DIAO Ming-jun, XU Lan-lan, YUE Shu-bo, ZHAO Jing. A new algebra method for constructing exact solutions of nonlinear evolution equations[J]. J4, 2012, 29(3): 279-285.

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