应用(1/G)-展开法求解五阶KdV方程(英文)

Application of the (1/G)-expansion Method to the Generalized Fifth Order KdV Equation

本篇论文首次提出(1/G)-展开法,用于求解非线性演化方程的行波解.将该法应用于五阶KdV方程的求解,当参数满足一定条件时,该方程可化为Sawada-Kotera(SK)方程、Caudrey-Dodd-Gibbon(CDG)方程、Kaup-Kupershmidt(KK)方程、Lax方程和Ito方程.其解可被表示为含两个任意参数的双曲函数解和三角函数解,作为示例,文中仅给出了SK方程和Ito方程的行波解.(1/G)-展开法具有直接、简捷与基本的特点,可以适用于数学物理中其它非线性演化方程的求解.

The （1/G）-expansion method is proposed to find travelling wave solutions of the generalized fifth order KdV equation（fKdV） which can become the Sawada-Kotera（SK） equation,Caudrey-Dodd-Gibbon（CDG） equation,Kaup-Kupershmidt（KK） equation,Lax equation and Ito equation if the coefficients of the fKdV are taken as the different values,respectively.As a result,exact travelling wave solutions expressed by hyperbolic functions and trigonometric functions with two arbitrary constants of the fKdV are obtained provided its coefficients satisfy a constraint condition,based on which the travelling wave solutions of mentioned several special forms of the fKdV can also be derived,as illustrative examples,the travelling wave solutions of the SK equation and Ito equation are given here.The proposed method is direct,concise and elementary,and it can be used for other nonlinear evolution equations in mathematical physics.