The Application of the Homotopy Analysis Method and the Homotopy Perturbation Method to the Davey-Stewartson Equations and Comparison between Them and Exact Solutions

Abstract

We introduce two powerful methods to solve the Davey-Stewartson equations: one is the homotopy perturbation method (HPM) and the other is the homotopy analysis method (HAM). HAM is a strong and easy to use analytic tool for nonlinear problems. Comparison of the HPM results with the HAM results, and compute the absolute errors between the exact solutions of the DS equations with the HPM solutions and HAM solutions are obtained.

On the exact solutions of the fractional (2+1)- dimensional Davey - Stewartson equation system

“…In the context, q(x, y, t) is the amplitude of a surface wave packet, while φ(x, y) represents the velocity potential of the mean flow interacting with the surface wave [10]. Although the classical Davey-Stewartson equation had been studied many times, the studies for fractional Davey-Stewartson equation was started newly [11][12][13].…”