Solution of the Nonlinear Schrödinger Equation with Defocusing Strength Nonlinearities Through the Laplace–Adomian Decomposition Method

In this work we apply the Adomian decomposition method combined with the Laplace transform (LADM) in order to solve the 1-dimensional nonlinear Schrödinger equation whose nonlinear term presents a nonlinear defocusing strength that varies in the spatial direction. The suggested iterative scheme (LADM) finds the solution without any discretization, linearization or restrictive assumptions. Finally, three numerical examples are presented to demonstrate the reliability and accuracy of the method.