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

Fabrice Bethuel (1) , Philippe Gravejat (2) , Jean-Claude Saut (3)

1 LJLL - Laboratoire Jacques-Louis Lions
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
3 LM-Orsay - Laboratoire de Mathématiques d'Orsay

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).

Mots clés: Gross-Pitaevskii equation; travelling wave; Kadomtsev-Petviashvili equation

Domaines: Equations aux dérivées partielles [math.AP]

Fabrice Bethuel, Philippe Gravejat, Jean-Claude Saut. On the KP I transonic limit of two-dimensional Gross-Pitaevskii travelling waves. Dynamics of Partial Differential Equations, 2008, 5 (3), pp.241-280. ⟨10.4310/DPDE.2008.v5.n3.a3⟩. ⟨hal-00285751v2⟩