New Solutions for Nonlinear Schrodinger Equations using Adomian Decomposition and Homotopy Perturbation Methods

Abstract

Coupled non-linear Schrodinger equation (CNLS) with two mode propagations in an optical fibre was studied. Using Painleve analysis, we are successfully solving the focusing Manakov system, bright and dark solitons using Adomian Decomposition Method (ADM) and Homotopy Perturbation Method (HPM). Both methods are fast convergent, do not need linearization and eliminates massive computation work. Its hows that HPM does not involve the Adomian polynomials when dealing with non-linear problems.