广义四阶色散方程的对称约化和精确解

J4 ›› 2014, Vol. 31 ›› Issue (3): 264-272.

广义四阶色散方程的对称约化和精确解

王振立, 刘希强

聊城大学数学科学学院，山东聊城 252059

出版日期:2014-05-28 发布日期:2014-05-27
通讯作者: 刘希强(1957- ),山东菏泽人,教授,博士,研究方向为非线性偏微分方程系统。 E-mail:liuxiq@sina.com
作者简介:王振立山东枣庄人,硕士,主要从事非线性偏微分方程解的研究。E-mail: rr101014@163.com
基金资助:
supported by National Natural Science Foundation of China and China Academy of Engineering Physics (11076015)

Symmetry reduction and exact solutions of a generalized fourth-order dispersive equation

Wang Zhen-li, Liu Xi-qiang

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

Published:2014-05-28 Online:2014-05-27

摘要/Abstract

摘要： 运用经典对称方法解决广义四阶色散方程问题,得到对称约化和群不变解,包括双曲函数解，三角周期解和孤立子解.最后得出了该问题的守恒律.

关键词: 非线性方程, 孤立子解, 李点对称, 对称约化, 守恒律

Abstract: By applying the direct symmetry method to a generalized fourth-order dispersive equation, we obtain the symmetry reductions, group invariant solutions of this equation, which include hyperbolic function solutions, trigonometric function solutions and soliton solution. At last, we give the conservation laws of this equation.

Key words: nonlinear equation, soliton solution, Lie point symmetry groups, symmetry reduction, conservation laws

中图分类号:

O175.2

王振立, 刘希强. 广义四阶色散方程的对称约化和精确解[J]. J4, 2014, 31(3): 264-272.

Wang Zhen-li, Liu Xi-qiang. Symmetry reduction and exact solutions of a generalized fourth-order dispersive equation [J]. J4, 2014, 31(3): 264-272.

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