# 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} }

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…

## 60 Citations

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