（3+1）维广义KdV-Zakharov-Kuznetsev方程的对称、约化和精确解

J4 ›› 2014, Vol. 31 ›› Issue (6): 670-677.

（3+1）维广义KdV-Zakharov-Kuznetsev方程的对称、约化和精确解

于兴江

聊城大学数学科学学院，山东聊城 252059

收稿日期:2014-03-10 修回日期:2014-03-19 出版日期:2014-11-28 发布日期:2014-11-17
通讯作者: 于兴江（1961—）山东莒县人，副教授，主要从事微分方程理论及应用研究 E-mail:yuxj10086@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项目(11076015)

Symmetries, reductions and exact solutions of KdV-Zakharov-Kuznetsev equation

YU Xingjiang

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

Received:2014-03-10 Revised:2014-03-19 Published:2014-11-28 Online:2014-11-17

摘要/Abstract

摘要： 利用直接对称方法得到了广义KdV-Zakharov-Kuznetsev方程（简写为mKdV-ZK）的对称约化、精确解，其中包括椭圆函数解，幂级数解，艾米儿函数解等. 利用得到的对称，求出了该方程的守恒律.

关键词: 非线性方程, mKdV-ZK方程, 直接对称法, 相似约化, 精确解, 守恒律

Abstract: By applying a direct symmetry method, the symmetry reduction, group invariant solution and many new exact solutions of the modified KdV-Zakharov-Kuznetsev equation (mKdV-ZK for short) are obtained, which include Jacobi elliptic function solutions, hyperbolic function solutions, trigonometric function solutions and so on. The conservation laws are derived at last.

Key words: nonlinear equation, mKdV-ZK equation, direct symmetry method, symmetry reduction, exact solution, conservation laws

中图分类号:

O175.2

于兴江. （3+1）维广义KdV-Zakharov-Kuznetsev方程的对称、约化和精确解[J]. J4, 2014, 31(6): 670-677.

YU Xingjiang. Symmetries, reductions and exact solutions of KdV-Zakharov-Kuznetsev equation[J]. J4, 2014, 31(6): 670-677.

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