Journal of Nonlinear Science

, Volume 6, Issue 2, pp 139–145 | Cite as

Nonexistence of travelling wave solutions to nonelliptic nonlinear schrödinger equations

  • J. M. Ghidaglia
  • J. C. Saut


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).


Cauchy Problem Wave Solution Travel Wave Solution Positive Radial Solution Inverse Scattering Transform 
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Copyright information

© Springer-Verlag New York Inc 1996

Authors and Affiliations

  • J. M. Ghidaglia
    • 1
  • J. C. Saut
    • 2
  1. 1.E.N.S. de Cachan, CMLA, URA 1611 du CNRSCachanFrance
  2. 2.Université des Paris-Sud et CNRS, URA 760OrsayFrance

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