Heteroclinic standing waves in defocusing DNLS equations: variational approach via energy minimization

Abstract

We study heteroclinic standing waves (dark solitons) in discrete nonlinear Schrödinger equations with defocusing 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.

Keywords:

• discrete nonlinear Schrödinger equation (DNLS)
• nonlinear lattice waves
• variational methods
• heteroclinic standing waves
• dark solitons

AMS Subject Classifications:

• 37K60
• 47J30
• 78A40