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Instability for the Semiclassical Non-linear Schrödinger Equation

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Abstract

We adapt recent results on instability for non-linear Schrödinger equations to the semi-classical setting. Rather than work with Sobolev spaces we estimate projective instability in terms of the small constant, h, appearing in the equation. Our motivation comes from the Gross-Pitaevski equation used in the study of Bose-Einstein condensation.

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Authors and Affiliations

  1. Université Paris Sud, Mathématiques, Bât. 425, 91405, Orsay Cedex, France

    Nicolas Burq

  2. Institut Universitaive de France,  

    Nicolas Burq

  3. Mathematics Department, University of California, Evans Hall, Berkeley, CA, 94720, USA

    Maciej Zworski

Authors
  1. Nicolas Burq
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  2. Maciej Zworski
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Correspondence to Nicolas Burq.

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Communicated by P. Constantin

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Burq, N., Zworski, M. Instability for the Semiclassical Non-linear Schrödinger Equation. Commun. Math. Phys. 260, 45–58 (2005). https://doi.org/10.1007/s00220-005-1402-x

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  • DOI: https://doi.org/10.1007/s00220-005-1402-x

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