Quasi-periodic solutions of nonlinear random Schr\"odinger equations

TL;DR

This paper develops a method to construct quasi-periodic solutions for nonlinear random Schrödinger equations on lattices, using advanced mathematical techniques to handle randomness and nonlinearity.

Contribution

It introduces a novel approach combining Lyapunov-Schmidt decomposition and multiscale Newton scheme for these equations.

Findings

Successfully constructs quasi-periodic solutions on a set of positive measure.

Demonstrates the effectiveness of the combined mathematical techniques.

Provides a framework for analyzing nonlinear random Schrödinger equations.

Abstract

We construct quasi-periodic solutions to the lattice nonlinear random Schroedinger equation on a set of potentials of positive measure via using a Lyapunov-Schmidt decomposition and a multiscale Newton scheme.