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}
}
Comments
12 pages