对称正则长波方程组的对称,精确解和守恒律

J4 ›› 2012, Vol. 29 ›› Issue (1): 21-26.

对称正则长波方程组的对称,精确解和守恒律

陈美, 刘希强, 王猛

聊城大学数学科学学院，山东聊城 252059

出版日期:2012-01-28 发布日期:2012-01-28
通讯作者: 刘希强（1957—），山东菏泽人，教授，博士，研究方向为非线性微分方程系统。 E-mail:liuxiq@sina.com.cn
作者简介:陈美（1984—），女，研究生，研究方向为非线性发展方程。E-mail:chenmei-777@163.com
基金资助:
国家自然科学基金和中国工程物理研究院联合基金资助（11076015）

Exact solutions and conservation laws of Symmetric Regularized Long Wave(SRLW) equations

Chen Mei，Liu Xiqiang，Wang Meng

School of Mathematical Sciences, Liaocheng University, Liaocheng 252059, China

Published:2012-01-28 Online:2012-01-28

摘要/Abstract

摘要：

通过利用修正的CK直接约化方法,建立了SRLW方程组的对称群理论。利用对称群理论建立了SRLW方程组的新旧解之间的关系,从而利用SRLW方程组的旧解得到了它们的新的精确解。基于上述理论和SRLW方程组的共轭方程组的解,得到了SRLW方程组的守恒律。

关键词: 非线性发展方程, 精确解, 守恒律, 修正的CK直接约化方法

Abstract:

By using the modified direct method, we derive the symmetry group theorem to SRLW equations. Some new exact solutions of SRLW equations are obtained by applying our theorem and given solutions. Also we get conservation laws of the equations with the corresponding Lie symmetry.

Key words: nonlinear evolution equation, exact solutions, conservation laws, CK’s direct method

中图分类号:

O175

陈美, 刘希强, 王猛. 对称正则长波方程组的对称,精确解和守恒律[J]. J4, 2012, 29(1): 21-26.

Chen Mei，Liu Xiqiang，Wang Meng. Exact solutions and conservation laws of Symmetric Regularized Long Wave(SRLW) equations[J]. J4, 2012, 29(1): 21-26.

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