Modulational Instabilities and Domain Walls in Coupled Discrete Nonlinear Schr\"odinger Equations

TL;DR

This paper investigates modulational instabilities and domain wall solutions in a system of coupled discrete nonlinear Schrödinger equations, providing criteria for instability and exploring specific solution types relevant to physical systems.

Contribution

It derives a modulational instability criterion for coupled discrete nonlinear Schrödinger equations and analyzes domain-wall solutions with linear coupling.

Findings

Derived a modulational instability criterion for plane-wave solutions.

Identified and examined domain-wall solutions in the presence of linear coupling.

Provided insights into physical relevance of the model cases.

Abstract

We consider a system of two discrete nonlinear Schr\"{o}dinger equations, coupled by nonlinear and linear terms. For various physically relevant cases, we derive a modulational instability criterion for plane-wave solutions. We also find and examine domain-wall solutions in the model with the linear coupling.