  We prove the existence of nontrivial finite energy traveling waves for a
large class of nonlinear Schr\"odinger equations with nonzero conditions at
infinity (includindg the Gross-Pitaevskii and the so-called "cubic-quintic"
equations) in space dimension $ N \geq 2$. We show that minimization of the
energy at fixed momentum can be used whenever the associated nonlinear
potential is nonnegative and it gives a set of orbitally stable traveling
waves, while minimization of the action at constant kinetic energy can be used
in all cases. We also explore the relationship between the families of
traveling waves obtained by different methods and we prove a sharp nonexistence
result for traveling waves with small energy.
