Stability of discrete dark solitons in nonlinear Schrodinger lattices

TL;DR

This paper investigates the stability of discrete dark solitons in nonlinear Schrödinger lattices, deriving a new stability criterion from the anti-continuum limit and confirming it through numerical analysis.

Contribution

It introduces a novel stability criterion for discrete dark solitons and provides detailed eigenvalue calculations with numerical validation.

Findings

Derived a stability/instability criterion for dark solitons

Confirmed the criterion through numerical simulations

Achieved good agreement between asymptotic predictions and numerical data

Abstract

We obtain new results on the stability of discrete dark solitons bifurcating from the anti-continuum limit of the discrete nonlinear Schrodinger equation, following the analysis of our previous paper [Physica D 212, 1-19 (2005)]. We derive a criterion for stability or instability of dark solitons from the limiting configuration of the discrete dark soliton and confirm this criterion numerically. We also develop detailed calculations of the relevant eigenvalues for a number of prototypical configurations and obtain very good agreement of asymptotic predictions with the numerical data.