Comparison Between The Homotopy Analysis Method And Homotopy Perturbation Method To Solve Two Dimensional Nonlinear Schr Odinger Equations With External Potentials

Abstract

Most of nonlinear partial di erential equations have many application in physical world. Moreover, the solutions of nonlinear partial di erential equations are not easily solvable and hence di erent methods were applied to get solutions of such nonlinear partial di erential equations. Among them, We considered the homotopy analysis and homotopy perturbation and their comparison. These methods were successfully implemented in solving the two dimensional nonlinear Schr odinger equations with external potential and the obtained solutions were compared. Furthermore, we considered di erent parameters to investigate the nature of solutions in graphical manner. Finally, the proposed methods are standard, e ective and easily compared in solving the two dimensional nonlinear Schr odinger equations with external potentials