Traveling waves for nonlinear schröodinger equations with nonzero conditions at infinity

Abstract

For a large class of nonlinear Schröodinger equations with nonzero conditions at infinityand 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 ≥ 3. Our results are valid as well for the Gross-Pitaevskii equation and for NLS with cubic-quintic nonlinearity. © 2013 Department of Mathematics, Princeton University.