The homotopy analysis method (HAM) is applied to solve the nonlinear Schrödinger (NLS)
equations. In this paper, we will reduce the NLS equation to a system of two nonlinear
equations contain the real and imaginary parts of the solution. The method provides the
solution in the form of a rapidly convergent series with easily computable components using
symbolic computation software such as Mathematica. The scheme shows importance of
choice of convergence-control parameter ħ to guarantee the convergence of the solutions of
nonlinear differential equations. This scheme is tested on two cases study, the cubic nonlinear
Schrödinger (CNLS) equation and a system of coupled nonlinear Schrödinger equations. The
results demonstrate reliability and efficiency of the algorithm developed. |
