He's Homotopy Perturbation Method for Solving Coupled- KdV Equations

Abstract

The homotopy perturbation technique is an analytical procedure for finding the solutions of differential equations, which is based on the constructing of a homotopy with an embedding parameter p is an element of [0,1], and this parameter is used as an expanding parameter. The approximations obtained by the method are uniformly valid not only for small parameters, but also for very large parameters. The fact that this technique, in contrary to the traditional perturbation methods, does not require a small parameter in the system, leads to wide applications in non-linear equations.