HPM AND VIM METHODS FOR FINDING THE EXACT SOLUTIONS OF THE NONLINEAR DISPERSIVE EQUATIONS AND SEVENTH-ORDER SAWADA–KOTERA EQUATION

In this paper, nonlinear dispersive equations and seventh-order Sawada–Kotera equation are solved using homotopy perturbation method (HPM) and variational iteration method (VIM). The results obtained by the proposed methods are then compared with that of Adomian decomposition method (ADM). The comparisons demonstrate that the two obtained solutions are in excellent agreement. The numerical results calculated show that the methods can be accurately implemented to these types of nonlinear equations. The results of HPM and VIM confirm the correctness of those obtained by Adomian decomposition method.