Eur. Phys. J. B 1, 245-253 (1998)
https://doi.org/10.1007/s100510050178

Nonlinear Schrödinger equation and superfluid hydrodynamics

Laboratoire de Physique, ENS-Lyon (URA CNRS 1325) , 46 allée d'Italie, 69364 Lyon Cedex 07, France

Corresponding author: ^a coste@physique.ens-lyon.fr

Received: 19 August 1997
Revised: 16 October 1997
Accepted: 6 November 1997
Published online: 15 January 1998

Abstract

We show that it is possible to generalize the Gross-Pitaevskii equation describing superfluidity in order to recover the two-fluid model, in the hydrodynamic limit, when the deviations from the equilibrium state are of long wavelength. When short distances are relevant, it is possible to keep trace of the purely quantum, non-hydrodynamic term of the Gross-Pitaevskii equation, so that the Hills-Roberts model, which describes the healing phenomenon, is finally obtained.