Traveling waves for nonlinear Schrödinger equations with nonzero conditions at infinity

Abstract

For a large class of nonlinear Schrödinger 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 $N\ge 3$. Our results are valid as well for the Gross-Pitaevskii equation and for NLS with cubic-quintic nonlinearity.

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