(1+1)维GSWW方程的新显式精确解

New Explicit Exact Solutions for the (1+1)-Dimensional Generalized Shallow Water Wave Equation

摘要: 本文以(G'/G)展开法的基本思路为依据，构造了一类f(G,G')形式的展开法，其中的G函数是由一类二阶非线性的常微分方程的显式解得到。用此展开法对(1+1)维GSWW方程进行研究，求得了该方程多种形式的新精确行波解。事实证明，这类f(G,G')展开法对于求得非线性偏微分方程多种形式的显式精确解非常有效。

Abstract: In this paper, based on the basic idea of the (G'/G) expansion method, a class f(G,G') expansion method is constructed, in which the G functions are obtained by explicit solutions of a class of two order nonlinear ordinary differential equations. With this method to research the (1+1)-dimensional generalized shallow water wave equation, many forms of new travelling wave solutions are obtained. It is proved that the f(G,G') expansion method is very effective for obtaining explicit and exact solutions of many forms of nonlinear partial differential equations.