Exp-展开法与变系数非线性发展方程的精确解

J4 ›› 2016, Vol. 33 ›› Issue (6): 680-688.

Exp-展开法与变系数非线性发展方程的精确解

王晓利¹,斯仁道尔吉²

内蒙古师范大学数学科学学院，内蒙古呼和浩特，010022

收稿日期:2016-06-07 修回日期:2016-07-24 出版日期:2016-11-28 发布日期:2016-11-28
通讯作者: 斯仁道尔吉（1954-），内蒙古正蓝旗人，教授，博士，研究方向：孤立子与可积系统理论及其应用 E-mail:siren@imnu.edu.cn.

Exp-Expansion Method and Exact Solutions of Two Variable Coefficients Nonlinear Evolution Equations

Wang Xiao-li, Sirendaoerji

College of Mathematics Science, Inner Mongolia Normal University, Hohhot 010022, China

Received:2016-06-07 Revised:2016-07-24 Published:2016-11-28 Online:2016-11-28

摘要/Abstract

摘要： Exp-展开法运用于求解变系数非线性发展方程并以广义变系数KdV-mKdV方程和变系数（2+1）维Broer-Kaup方程组为例实现了求解过程，获得了奇异行波解，包括指数函数解、双曲函数解、三角函数解及有理函数解，并通过取特殊值得到熟知的kink型解。由此说明Exp(-?(?))-展开法不仅适用于常系数非线性发展方程的求解，还适用于变系数非线性发展方程的求解并且更具有一般性。

关键词: 变系数非线性发展方程； -展开法；精确解；非线性光纤通讯

Abstract: The Exp-expansion method is used successfully to solve a generalized variable coef?cients KdV–mKdV equation and (2+1)–dimensional Broer-Kaup equation.The singular travelling wave solutions are expressed in terms of the exponential functions,the hyperbolic functions,the trigonometric functions and the rational functions.When parameters are taken to be special values,the kink type solitary wave solutions are derived. It is shown that the Exp(-?(?))-expansion method is not only appropriate for solving nonlinear evolution equations with constant coefficients but also applicable to solve the nonlinear evolution equations with variable coefficients.

Key words: nonlinear evolution equation with variable coefficients; exact solutions; -expansion method; fibre-optical communication

中图分类号:

O175.29

王晓利斯仁道尔吉. Exp-展开法与变系数非线性发展方程的精确解[J]. J4, 2016, 33(6): 680-688.

Wang Xiao-li, Sirendaoerji. Exp-Expansion Method and Exact Solutions of Two Variable Coefficients Nonlinear Evolution Equations[J]. J4, 2016, 33(6): 680-688.

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