An Approximate Analytical Solution of the Nonlinear Schr?dinger Equation with Harmonic Oscillator Using Homotopy Perturbation Method and Laplace-Adomian Decomposition Method

摘要

The Laplace-Adomian Decomposition Method (LADM) and Homotopy Perturbation Method (HPM) are both utilized in this research in order to obtain an approximate analytical solution to the nonlinear Schr?dinger equation with harmonic oscillator. Accordingly, nonlinear Schr?dinger equation in both one and two dimensions is provided to illustrate the effects of harmonic oscillator on the behavior of the wave function.The available literature does not provide an exact solution to the problem presented in this paper.Nevertheless, approximate analytical solutions are provided in this paper using LADMandHPMmethods, in addition to comparing and analyzing both solutions.