Travelling waves for the Nonlinear Schrödinger Equation with nonzero condition at infinity.

We present two constraint minimization approaches to prove the existence of traveling waves for a wide class of nonlinear Schrödinger equations with nonvanishing conditions at infinity in space dimension N ≥ 2. Minimization of the energy at fixed momentum can be used whenever the associated potential function is positive on the natural function space and it gives a set of orbitally stable traveling waves. Minimization of the action at constant kinetic energy can be used in all cases, but gives no information on the orbital stability of the set of solutions.