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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