Traveling waves for nonlinear Schrödinger equations with nonzero conditions at infinity, II

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

2012-03-08

arxiv.org/abs/1203.1912v1

Mathematics

Analysis of PDEs

71 pages

Scientific paper

We present two constraint minimization approaches to prove the existence of traveling waves for a wide class of nonlinear Schr\"odinger equations with nonvanishing conditions at infinity in space dimension $ N \geq 2$. 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. Minimization of the action at constant kinetic energy can be used in all cases, but it gives no information about the orbital stability of the set of solutions.

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