on the convergence of the vhpm for the zakharove-kuznetsov equations

in this paper, the variational homotopy perturbation method (vhpm) and its convergence is adopted for thezakharove-kuznetsov equations (zk-equations). the aim of this paper is to present an efficient and reliabletreatment 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-kowalevskayatheorem of differential equations with analytical vector field.