利用推广的Tanh函数法求解两个非线性发展方程

中国民航大学学报

利用推广的Tanh函数法求解两个非线性发展方程

刘雪梅，接贤

（中国民航大学理学院，天津300300）

收稿日期:2014-03-26 修回日期:2014-05-12 出版日期:2015-08-22 发布日期:2015-09-24
作者简介:刘雪梅（1977—），女，黑龙江呼兰人，副教授，硕士，研究方向为代数方程.
基金资助:
中央高校基本科研业务费专项（3122013k001）

Applications of extended Tanh function method in two nonlinear evolution equations

LIU Xue-mei,JIE Xian

(College of Science,CAUC,Tianjin 300300,China)

Received:2014-03-26 Revised:2014-05-12 Online:2015-08-22 Published:2015-09-24

摘要/Abstract

摘要：

利用推广的Tanh 函数法，借助于符号计算系统Mathematica 求解获得了Kaup-Kupershmidt 方程和(2+1)-维Kdv-Burgers 方程新的精确行波解，并分别以含有两个任意参数的双曲函数解、三角函数解及有理函数解等3 种形式表示，其中双曲函数表示的行波解中参数取特殊值时可得到孤波解。

关键词: 推广的Tanh函数法, 行波解, Kaup-Kupershmidt方程, (2+1)-维Kdv-Burgers 方程

Abstract:

Algebraic method can directly and efficiently construct the exact solutions of nonlinear evolution equations,and the computing can be achieved by computer algebraic systems. A new exact traveling wave solution of Kaup-Kupershmidt equation and (2+1)-dimensional Kdv-Burgers equation is successfully constructed by using the extended Tanh function method. The exact traveling wave solution with double arbitrary parameters is respectively expressed by hyperbolic functions,trigonometric functions and rational functions. Some solitary wave solutions can be obtained from hyperbolic function solutions when the parameters are regarded as special values.

Key words: extended Tanh function method, traveling wave solutions, Kaup-Kupershmidt equation, (2+1)-dimensional Kdv-Burgers equation

中图分类号:

O175.29

刘雪梅，接贤. 利用推广的Tanh函数法求解两个非线性发展方程[J]. 中国民航大学学报.

LIU Xue-mei,JIE Xian. Applications of extended Tanh function method in two nonlinear evolution equations[J]. .

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