# American Institute of Mathematical Sciences

March  2021, 41(3): 1507-1517. doi: 10.3934/dcds.2020328

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

 1 Department of Mathematics and Statistics, Missouri University of Science & Technology, Rolla, MO, USA 2 Research Institute for Mathematical Sciences, Kyoto University, Kyoto, Japan

* Corresponding author: Jason Murphy

Received  July 2019 Revised  September 2019 Published  September 2020

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.

Citation: Jason Murphy, Kenji Nakanishi. Failure of scattering to solitary waves for long-range nonlinear Schrödinger equations. Discrete & Continuous Dynamical Systems, 2021, 41 (3) : 1507-1517. doi: 10.3934/dcds.2020328
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