Modification of Coupled Drinfel’d-Sokolov-Wilson Equation and Approximate Solutions by Optimal Perturbation Iteration Method

Abstract

We try to find the semi-analytical approximate solutions for the system of partial differential equationsby using a newly developed scheme. The optimal perturbation iteration method is introduced and thenapplied to a newly modified coupled Drinfel’d-Sokolov-Wilson equation. Classical perturbation theoryand optimization techniques are combined to construct this method. We will deeply analyze an exampleto prove the power of the proposed method, namely the optimal perturbation iteration method. Withthe theorem and applications, we see that the present study shows that the new method convergesfast to the accurate analytical solutions of the considered equations at even the first two-threeiterations.