Application of the homotopy perturbation method to Zakharov Kuznetsov equations

The aim of this paper is to apply the homotopy perturbation method (HPM) to solve the Zakharov Kuznetsov ZK(m; n; k) equations. The two special cases, ZK(2, 2, 2) and ZK(3, 3, 3), are chosen to show the ability of the method. General formulas for the solutions of ZK(m; n; k) are established. The results reveal that the method is very effective and simple.