Homotopy analysis and Homotopy Pad$acute{e}$ methods for two-dimensional coupled Burger's equations

this paper, analytic solutions of two-dimensional coupled Burger's equations are obtained by the Homotopy analysis and the Homotopy Pad$acute{e}$ 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 Pad$acute{e}$ technique is often independent of auxiliary parameter $hbar$ and this technique accelerate the convergence of the related series.