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Nonlinear PDE’s in Condensed Matter and Reactive Flows pp 339–354Cite as

Vortices and Sound Waves for the Gross-Pitaevskii Equation

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Part of the book series: NATO Science Series ((ASIC,volume 569))

Abstract

We consider the defocusing cubic nonlinear Schrödinger equation, known as the Gross-Pitaevskii equation in the context of superfluid Helium II at a temperature near zero. We survey recent rigorous mathematical results on travelling wave solutions, emphasizing the zero velocity and transonic limits.

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Author information

Authors and Affiliations

  1. Analyse Numérique, Université Pierre et Marie Curie, BC 187, 4 Place Jussieu, 75252, Paris Cedex 05, France

    F. Bethuel

  2. Département de Mathématiques, Université Paris-Sud, Bâtiment 425, 91405, Orsay, France

    J. C. Saut

Authors
  1. F. Bethuel
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  2. J. C. Saut
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Editor information

Editors and Affiliations

  1. Ecole des hautes Etudes en Sciences Sociales, Paris, France

    Henri Berestycki

  2. Ecole Normale Supérieure, CNRS, Paris, France

    Yves Pomeau

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Bethuel, F., Saut, J.C. (2002). Vortices and Sound Waves for the Gross-Pitaevskii Equation. In: Berestycki, H., Pomeau, Y. (eds) Nonlinear PDE’s in Condensed Matter and Reactive Flows. NATO Science Series, vol 569. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0307-0_15

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  • DOI: https://doi.org/10.1007/978-94-010-0307-0_15

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-0973-0

  • Online ISBN: 978-94-010-0307-0

  • eBook Packages: Springer Book Archive

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