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Failure of scattering to solitary waves for long-range nonlinear Schrödinger equations

  • * Corresponding author: Jason Murphy

    * Corresponding author: Jason Murphy 
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  • We consider nonlinear Schrödinger equations with either power-type or Hartree nonlinearity in the presence of an external potential. We show that for long-range nonlinearities, solutions cannot exhibit scattering to solitary waves or more general localized waves. This extends the well-known results concerning non-existence of non-trivial scattering states for long-range nonlinearities.

    Mathematics Subject Classification: Primary: 35Q55.


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