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

In this paper, analytic solutions of the modified Burgers-Korteweg-de Vries equation(mBKdVE) and the Newell-Whitehead equation are obtained by the Homotopyanalysis method(HAM) and the Homotopy Pade method(HPadeM). Theobtained approximation by using HAM contains an auxiliary parameter which is a way to control and adjust the convergence region and rate of the solution series.The approximation solution by [m, m] HPadeM is often independent of auxiliaryparameter h and this technique accelerate the convergence of the related series.