On the convergence of the VHPM for the Zakharove-Kuznetsov equations

Document Type: Regular Paper


Department of Mathematics, Faculty of Sciences, Mazandaran University, P.O. Box 47415-95447, Babolsar, Iran


In this paper, the variational homotopy perturbation method (VHPM) and its convergence is adopted for the
Zakharove-Kuznetsov equations (ZK-equations). The aim of this paper is to present an efficient and reliable
treatment of the VHPM for the nonlinear partial differential equations and show that this method is convergent.
The convergence of the applied method is approved using the method of majorants from Cauchy-Kowalevskaya
theorem of differential equations with analytical vector field.