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

Jason Murphy; Kenji Nakanishi

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arXiv · 1906.01802

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

Jason Murphy·Kenji Nakanishi

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Abstract

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.

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Jason Murphy, Kenji Nakanishi. 2019-06-05. Failure of scattering to solitary waves for long-range nonlinear Schrödinger equations. https://arxiv.org/abs/1906.01802

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