Homotopy analysis and Homotopy Pade methods for the modified Burgers-Korteweg-de Vries and the Newell-Whitehead equations

In this paper, analytic solutions of the modifiedBurgers-Korteweg-de Vries equation(mBKdVE) and theNewell-Whitehead equation are obtained by the Homotopy analysismethod(HAM) and the Homotopy Pad$acute{e}$method(HPad$acute{e}$M). The obtained approximation by using HAMcontains an auxiliary parameter which is a way to control and adjustthe convergence region and rate of the solution series. Theapproximation solution by $[m,m]$ HPad$acute{e}$M is oftenindependent of auxiliary parameter $ar{h}$ and this techniqueaccelerate the convergence of the related series.