Homotopy analysis and homotopy Padé methods for (1+1) and (2+1)‐dimensional dispersive long wave equations

Purpose The purpose of this paper is to obtain analytic solutions of the (1+1) and (2+1)‐dimensional dispersive long wave equations by the homotopy analysis and the homotopy Padé methods. Design/methodology/approach The obtained approximation by using homotopy method contains an auxiliary parameter which is a simple way to control and adjust the convergence region and rate of solution series. Findings The approximation solutions by [m,m] homotopy Padé technique is often independent of auxiliary parameter ℏ and this technique accelerates the convergence of the related series. Originality/value In this paper, analytic solutions of the (1+1) and (2+1)‐dimensional dispersive long wave equations are obtained by the homotopy analysis and the homotopy Padé methods. The obtained approximation by using homotopy method contains an auxiliary parameter which is a simple way to control and adjust the convergence region and rate of solution series. The approximation solutions by [m,m] homotopy Padé technique are often independent of auxiliary parameter ℏ and this technique accelerates the convergence of the related series.