Numerical simulation of fifth order KdV equations occurring in magneto-acoustic waves

Abstract

In this work, we aim to apply a numerical approach based on Homotopy perturbation transform method (HPTM) for derive the exact and approximate solutions of nonlinear fifth order KdV equations for study magneto-acoustic waves in plasma. The approach is a mixed form of the standard Laplace transform with the classical Homotopy perturbation technique. Nonlinear term can be handled with the aid of He's Polynomials. In this technique, the solution is calculated in the form of a convergent series and convergence of the HPTM solutions to the exact solutions is shown. The Homotopy perturbation transform method presents a wide applicability to handling nonlinear wave equations in science and engineering. As a novel application of HPTM, the present work shows some essential difference with the existing similar method. Several examples are provided for illustrate the simplicity and reliability of the method and highlighted the significance of this work. Keywords: Laplace transform, Homotopy perturbation method, Fifth order KdV equation, Non-homogeneous KdV equation, He's Polynomials