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,km,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,km,n,k) are established. The results reveal that the method is very effective and simple.