ON THE LINEAR WAVE REGIME OF THE GROSS-PITAEVSKII EQUATION

Fabrice Bethuel (1) , Raphaël Danchin (2) , Didier Smets (1)

1 LJLL - Laboratoire Jacques-Louis Lions
2 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

We study long-wavelength asymptotics for the Gross-Pitaevskii equation corresponding to perturbations of a constant state of modulus one. We exhibit lower bounds on the first occurrence of possible zeros (vortices) and compare the solutions with the corresponding solutions to the linear wave equation or variants. The results rely on the use of the Madelung transform, which yields the hydrodynamical form of the Gross-Pitaevskii equation, as well as of an augmented system.

Domaines: Physique mathématique [math-ph]

Fabrice Bethuel, Raphaël Danchin, Didier Smets. ON THE LINEAR WAVE REGIME OF THE GROSS-PITAEVSKII EQUATION. Journal d'analyse mathématique, 2010, 110 (?), pp.297--338. ⟨10.1007/s11854-010-0008-1⟩. ⟨hal-00693037⟩