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

Jason Murphy; Kenji Nakanishi

doi:10.3934/dcds.2020328

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2021, Volume 41, Issue 3: 1507-1517. Doi: 10.3934/dcds.2020328

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

Jason Murphy^1, , and
Kenji Nakanishi^2,

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
^* Corresponding author: Jason Murphy

Received: June 30, 2019

Revised: August 31, 2019

Early access: September 2020

Published: March 2021

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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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Mathematics Subject Classification: Primary: 35Q55.

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References

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