广义(G′/G)-展开法及其对Whitham-Broer-Kaup-Like方程组的应用(英文)

A Generalized(G′/G)-Expansion Method and Its Applications to the Whitham-Broer-Kaup-Like Equations

基于一种二阶变系数线性常微分方程,推出寻找非线性发展方程(组)精确解的广义(G′/G)-展开法及其算法.为检验简洁明了,该方法被应用于Whitham-Broer-Kaup-Like方程组,使得其包括双曲函数解、三角函数解和有理解的诸多新非行波解,并且这些解均在某些点处是非奇异的.该方法也适用于数学物理中的其他非线性发展方程(组).

Based on a homogeneous second order linear differential equation with variable coefficient,ageneral-ized（G′/G）-expansion method and its algorithm are proposed to seek exact solutions of nonlinear evolution equations.Being concise and straight forward,the method is applied to the Whitham-Broer-Kaup-Like equations.As aresult,many new non-travelling wave solutions are obtained,which contain the hyperbolic function solutions,the trigonometric function solutions and the rational solutions,and they are all nonsingular at some points.This method can be used for many other nonlinear evolution equations in mathematical physics.