# Traveling Waves for Nonlinear Schrödinger Equations with Nonzero Conditions at Infinity

@article{Mari2008TravelingWF,
title={Traveling Waves for Nonlinear Schr{\"o}dinger Equations with Nonzero Conditions at Infinity},
author={Mihai Mariş},
journal={Archive for Rational Mechanics and Analysis},
year={2008},
volume={226},
pages={143-242}
}
• M. Mariş
• Published 17 October 2008
• Mathematics
• Archive for Rational Mechanics and Analysis
We prove the existence of nontrivial finite energy traveling waves for a large class of nonlinear Schrödinger equations with nonzero conditions at infinity (includindg the Gross–Pitaevskii and the so-called “cubic-quintic” equations) in space dimension $${ N \geq 2}$$N≥2. We show that minimization of the energy at fixed momentum can be used whenever the associated nonlinear potential is nonnegative and it gives a set of orbitally stable traveling waves, while minimization of the action at…
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