Numerical Optics Soliton Solution of the Nonlinear Schrödinger Equation Using the Laplace and the Modified Laplace Decomposition Method

In this paper, the Laplace decomposition method (LDM) and some modification, namely the Modified Laplace decomposition method (MLDM), are adopted to numerically investigate the optic soliton solution of the nonlinear complex Schrödinger equation (NLSE). The obtained results demonstrate the reliability and the efficiency of the considered methods to numerically approximate such initial value problems (IVPs).