Traveling waves for nonlinear Schr\"odinger equations with nonzero conditions at infinity

Mihai Mariş

Traveling waves for nonlinear Schr\"odinger equations with nonzero conditions at infinity

Analysis of PDEs 2013-04-02 v2

Authors: Mihai Mariş

Abstract

For a large class of nonlinear Schr\"odinger equations with nonzero conditions at infinity and for any speed $c$ less than the sound velocity, we prove the existence of nontrivial finite energy traveling waves moving with speed $c$ in any space dimension $N\geq 3$ . Our results are valid as well for the Gross-Pitaevskii equation and for NLS with cubic-quintic nonlinearity.

Keywords

traveling waves nonlinear Schrödinger equation nonzero conditions at infinity Gross-Pitaevskii equation cubic-quintic nonlinearity

Cite

@article{arxiv.0903.0354,
  title  = {Traveling waves for nonlinear Schr\"odinger equations with nonzero conditions at infinity},
  author = {Mihai Mariş},
  journal= {arXiv preprint arXiv:0903.0354},
  year   = {2013}
}

Comments

60 pages. Final version, to appear in the Annals of Mathematics

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