Title

Failure of Scattering to Solitary Waves for Long-Range Nonlinear Schrödinger Equations

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.

Department(s)

Mathematics and Statistics

Comments

Japan Society for the Promotion of Science, Grant JP17H02854

Keywords and Phrases

Failure of scattering; Long-range nonlinearities; Nonlinear Schrödinger equations

International Standard Serial Number (ISSN)

1078-0947; 1553-5231

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2021 American Institute of Mathematical Sciences (AIMS), All rights reserved.

Publication Date

01 Mar 2021

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