Lattice Approximations to NLS

TL;DR

This paper proves that solutions of a discrete nonlinear Schrödinger lattice model with specific initial data converge to solutions of a coupled cubic NLS system, bridging discrete and continuous models.

Contribution

It introduces a rigorous convergence result for discrete NLS solutions to a coupled continuous NLS system for certain initial conditions.

Findings

Discrete NLS solutions converge to coupled cubic NLS solutions

Convergence holds for $L^2$ initial data with double frequency components

Establishes a link between lattice models and continuous NLS equations

Abstract

In this paper, we prove that solutions of the discrete NLS lattice model for $L^2$ initial data with double frequency components converge to solutions of a coupled system of cubic NLS.