English

Failure of scattering to solitary waves for long-range nonlinear Schr\"odinger equations

Analysis of PDEs 2021-01-11 v1

Abstract

We consider nonlinear Schr\"odinger 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.

Keywords

Cite

@article{arxiv.1906.01802,
  title  = {Failure of scattering to solitary waves for long-range nonlinear Schr\"odinger equations},
  author = {Jason Murphy and Kenji Nakanishi},
  journal= {arXiv preprint arXiv:1906.01802},
  year   = {2021}
}

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12 pages