Solution of the Nonlinear Schrodinger Equation with Defocusing Strength Nonlinearities Through the Laplace-Adomian Decomposition Method

TL;DR

This paper introduces a combined Laplace-Adomian decomposition method to solve the 1D nonlinear Schrödinger equation with spatially varying defocusing nonlinearities, avoiding discretization or linearization.

Contribution

The paper presents a novel application of the Laplace-Adomian decomposition method to nonlinear Schrödinger equations with spatially varying nonlinearities, providing an efficient analytical solution approach.

Findings

Method accurately solves the nonlinear Schrödinger equation.

Numerical examples confirm the reliability and precision of the approach.

The approach avoids discretization and linearization, simplifying computations.

Abstract

In this work we apply the Adomian decomposition method combined with the Laplace transform (LADM) in order to solve the 1-dimensional nonlinear Schrodinger 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.