G'/G-展开法及其在Burgers-KdV方程精确解中的应用

The Extended G'/G-expansion Method and Exact Solutions of Nonlinear Coupled KdV Equations

本文以数学机械化思想为指导,以计算机代数系统软件Maple为工具,提出了用G'/G-展法来构造非线性孤子方程的行波解。为了验证方法的有效性和优越性,将其应用到Burgers-KdV方程,获得了具有一般形式的新的精确解,其中包括新的双曲函数解以及三角函数解。

This paper try to improve the G＇/G-expansion method for constructing travelling wave solutions of nonlinear soliton equations under the guidance of mathematics mechanization and with the tools of transformation and computer algebraic system Maple. In order to illustrate the effectiveness and advantages of the method,the author applies it in the Burgers-KdV equation. Many new and general formal exact solutions are obtained including the hyperbolic function solutions and trigonometric function solutions.