Traveling waves for nonlinear Schrödinger equations with nonzero conditions at infinity

2009/03/02 by Mihai Mariş, Mariş, Mihai
Mathematics · Physics and Astronomy · #35B65 #35J15 #35J20 #35Q40 #35Q51 #35Q55 #37K40 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Cold Atom Physics and Bose-Einstein Condensates #FOS: Mathematics #Nonlinear Photonic Systems

paper · pdf · doi:10.48550/arxiv.0903.0354

openalex publication_date 2009/03/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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≥ 3. Our results are valid as well for the Gross-Pitaevskii equation and for NLS with cubic-quintic nonlinearity.

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