求解高维非线性演化方程的一个新方法

A new method of solution to high-dimensional nonlinear evolution equation

将王明亮等人提出的一种新方法-(G′/G)扩展法推广到高维的非线性演化方程。作为其应用的一个例子,获得(2+1)维Konopelchenko-Dubovsky方程带有任意参数形式的双曲函数解,三角函数解和有理数解,通过适当选择的参数,很多已知的解能被重新得到。本扩展方法可以进一步应用到其它一大批高维的非线性演化方程。

The new method--（ G′/G ） expansion method--proposed by Wang Ming--liang and others is promoted to high--dimensional nonlinear evolution equation. As an example in application, the hyperbolic function solution, trigonometric function solution and rational number solution are worked out for（2＋1）--dimensional Konopelchenk--Dubovsky equation with any parameters. If the parameter is properly selected, many known solutions can be re--gained. This expansion method can be further applied to many othey high--dimensional nonlinear evolution equations.