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Nonexistence of travelling wave solutions to nonelliptic nonlinear schrödinger equations

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Summary

By deriving Pohojaev-type identities we prove that nonelliptic nonlinear Schrödinger equations do not admit localized travelling wave solutions. Similary, we prove that the Davey-Stewartson hyperbolic-elliptic systems do not support travelling wave solutions except for a specific range of the parameters that comprises the DS II focusing case (where the existence of lumps is well known).

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Authors and Affiliations

  1. E.N.S. de Cachan, CMLA, URA 1611 du CNRS, 61 Avenue du Président Wilson, 94235, Cachan, France

    J. M. Ghidaglia

  2. Université des Paris-Sud et CNRS, URA 760, Bâtiment 425, 91405, Orsay, France

    J. C. Saut

Authors
  1. J. M. Ghidaglia
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  2. J. C. Saut
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Communicated by Thanasis Fokas

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Ghidaglia, J.M., Saut, J.C. Nonexistence of travelling wave solutions to nonelliptic nonlinear schrödinger equations. J Nonlinear Sci 6, 139–145 (1996). https://doi.org/10.1007/BF02434051

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  • DOI: https://doi.org/10.1007/BF02434051

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