利用(Ge^(-kξ)/G')扩展法求解非线性发展方程的精确行波解(英文)

Extended (Ge^(-kξ)/G')-Expansion Method and Exact Travelling Wave Solutions of Evolution Equations

寻找非线性演化方程的精确孤波解是一项非常重要和困难的工作.该文提出了一个(Ge-kξ/G')扩展法,并利用其获得了非对称Nizhnik-Novikov-Veselov系统的精确行波解.与其他方法相比,该文所给的方法更直接、简明和高效,同时还可以用来求解数学物理中其他非线性发展方程的精确解.更重要的是,该方法还能够得到一些高维、高阶的非线性发展方程精确行波解和非行波解.

The work of seeking the exact solutions of nonlinear evolution equations is very important and difficult.In this paper,a extended（Ge^-kξ/G＇）-expansion method is proposed,by which the exact travelling wave solutions involving asymmetrical Nizhnik-Novikov-Veselov system are obtained.The proposed method is direct,concise and effective;it also can be used for other nonlinear evolution equations in mathematical physics.More importantly,this method can be used to obtain exact travelling wave solutions and non-travelling wave solutions of some high-dimensional and high-order nonlinear evolution equations.