Traveling waves for nonlinear Schrödinger equations with nonzero conditions at infinity

Details Traveling waves for nonlinear Schrödinger equations with nonzero conditions at infinity Traveling waves for nonlinear Schrödinger equations with nonzero conditions at infinity

2009-03-02

arxiv.org/abs/0903.0354v1

Mathematics

Analysis of PDEs

54 pages

Scientific paper

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 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.

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