Heteroclinic standing waves in defocussing DNLS equations -- Variational approach via energy minimization

TL;DR

This paper proves the existence of heteroclinic standing waves in defocusing discrete nonlinear Schrödinger equations using energy minimization, and explores their continuum limit and numerical approximation.

Contribution

It provides an elementary variational existence proof for monotone, odd standing waves in defocusing DNLS equations, including continuum and numerical analysis.

Findings

Existence of heteroclinic standing waves established

Energy minimization approach used for proof

Analysis of continuum limit and numerical methods

Abstract

We study heteroclinic standing waves (dark solitons) in discrete nonlinear Schr\"{o}dinger equations with defocussing nonlinearity. Our main result is a quite elementary existence proof for waves with monotone and odd profile, and relies on minimizing an appropriately defined energy functional. We also study the continuum limit and the numerical approximation of standing waves.