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

Michael Herrmann

Type: Article

Publication Date: 2010-09-16

Citations: 10

DOI: https://doi.org/10.1080/00036811.2010.492504

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.

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