Soliton solutions for the Korteweg-de Vries equation by homotopy analysis method

Abstract

This article solves the well-known Korteweg-de Vries equation by the homotopy analysis method, an analytical, totally explicit technique. By choosing a proper auxiliary parameter, the new series solution converges rapidly to the exact solution, with a simple way to adjust the convergence region. In addition, we show that a significant improvement of the convergence rate and region is achieved by applying homotopy-pad/'e approximants. The present method holds promise in providing soliton solutions for more complicated wave equations.