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On the linear wave regime of the Gross-Pitaevskii equation

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Abstract

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.

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Authors and Affiliations

  1. Laboratoire J.-L. Lions UMR 7598, Université Pierre et Marie Curie, 175 Rue Du Chevaleret, 75013, Paris, France

    Fabrice Béthuel & Didier Smets

  2. Lama, UMR 8050, Université Parisest, 61 Avenue Du Général De Gaulle, 94010, Créteil Cedex, France

    Raphaël Danchin

Authors
  1. Fabrice Béthuel
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  2. Raphaël Danchin
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  3. Didier Smets
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Correspondence to Fabrice Béthuel.

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Béthuel, F., Danchin, R. & Smets, D. On the linear wave regime of the Gross-Pitaevskii equation. JAMA 110, 297–338 (2010). https://doi.org/10.1007/s11854-010-0008-1

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  • DOI: https://doi.org/10.1007/s11854-010-0008-1

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