Dynamics of Partial Differential Equations

Volume 5 (2008)

Number 3

On the KP I transonic limit of two-dimensional Gross-Pitaevskii travelling waves

Pages: 241 – 280

DOI: https://dx.doi.org/10.4310/DPDE.2008.v5.n3.a3

Authors

Fabrice Béthuel (Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Paris, France)

Philippe Gravejat (Centre de Recherche en Mathématiques de la Décision, Université Paris Dauphine, Paris, France)

Jean-Claude Saut (Laboratoire de Mathématiques, Université Paris Sud, Orsay, France)

Abstract

We provide a rigorous mathematical derivation of the convergence in the long-wave transonic limit of the minimizing travelling waves for the two-dimensional Gross–Pitaevskii equation towards ground states for the Kadomtsev-Petviashvili equation (KP I).

Keywords

transonic limit, Kadomtsev-Petviashvili equation, Gross-Pitaevskii equation, travelling waves

2010 Mathematics Subject Classification

35-xx, 76-xx

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Published 1 January 2008