On analytical solutions of the ZK equation and related equations by using the generalized (G /G) -expansion method

The generalized (G /G)-expansion method with the aid of Maple is proposed to seek exact solutions of nonlinear evolution equations. For finding exact solutions are expressed three types of solutions that include hyperbolic function solution, trigonometric function solution and rational solution. The article study the Zakharov–Kuznetsov (ZK) equation, the generalized ZK (gZK) equation, and the generalized forms of these equations. Exact solutions with travelling wave solutions of nonlinear evolution equations are obtained. It is shown that the proposed method is direct, effective and can be used for many other nonlinear evolution equations. We use complicated computations by using Maple software.

Keywords:

Generalized (G /G )-expansion method , Zakharov–Kuznetsov equation , Generalized Zakharov-Kuznetsov equation , Travelling wave solution , Matlab and Maple software