mKDV-ZK方程的精确解

Exact Solutions for mKDV-ZK Equation

利用(G’/G)法求解了mKDV-ZK方程的精确解,得到了mKDV-ZK方程的用双曲函数,三角函数和有理函数表示的三类精确行波解.由于此方法中的G为某个二阶常系数线性ODE的通解,故方法具有直接、简洁的优点;更重要的是,这种方法可用于求得其它许多非线性演化方程的行波解.如果对其中双曲函数表示的行波解中的参数取特殊值,那么可得已有的孤波解.

The（G′/ G）method was used to solve the mKDV-ZK equation,by means of which three types of exact traveling wave solutions were obtained,including the hyperbolic functions,trigonometric and rational function solutions.In this method,G for a second order linear ODE of the general solution,so the method is direct,simple;more importantly,this method can be used in many other nonlinear evolution equations to obtain traveling wave solutions.If special values of the hyperbolic functions were taken,existed solitary wave solutions can be gotten.