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
