A new approach to find approximate solutions of system of NLPDEs arising in physics

Abstract

In this paper, we are concerned with finding approximate solutions to systems of nonlinear PDEs using the Reduced Differential Transform Method (RDTM). We examine this method to obtain approximate numerical solutions for four different types of systems of nonlinear partial differential equations, such as the homogeneous KdV equation of the third order types (I) and (II),
coupled Zakharov-Kuznetsov system and the coupled Burgers equation.
The theoretical analysis of the RDTM is investigated for these systems of equations and is calculated in the form of power series with easily computable terms. Illustrative examples will be presented to support the proposed method. The obtained results are in a good agreement with the exact solutions. This method reduces significantly the numerical computations compare with the existing methods such as the perturbation technique, differential transform method (DTM) and the Adomian decomposition method (ADM).