A numerical and symbolical approximation of the Nonlinear Anderson Model

TL;DR

This paper introduces a modified perturbation theory to solve the nonlinear Schrödinger equation with random potential, providing efficiency improvements and error estimates, applicable to other nonlinear differential equations in physics.

Contribution

It presents a novel perturbation approach for the nonlinear Anderson model, offering efficiency and error analysis not previously available.

Findings

The method is more efficient than existing approaches in certain cases.

Error estimates for the approximation are derived.

Applicable to other nonlinear differential equations in physics.

Abstract

A modified perturbation theory in the strength of the nonlinear term is used to solve the Nonlinear Schroedinger Equation with a random potential. It is demonstrated that in some cases it is more efficient than other methods. Moreover we obtain error estimates. This approach can be useful for the solution of other nonlinear differential equations of physical relevance.