Travelling wave-like solutions of the Zakharov-Kuznetsov equation with variable coefficients are studied using the solutions of Raccati equation. The solitary wave-like solution, the trigonometric periodic wave solution and the rational wave solution are obtained with a constraint between coefficients. The property of the solutions is numerically investigated. It is shown that the coefficients of the equation do not change the wave amplitude, but may change the wave velocity.

This paper studies the Klein–Gordon–Zakharov equation with power-law nonlinearity. This is a coupled nonlinear evolution equation. The solutions for this equation are obtained by the travelling wave hypothesis method, $(G'/G)$ method and the mapping method.