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.
Recommended Citation
J. Murphy and K. Nakanishi, "Failure of Scattering to Solitary Waves for Long-Range Nonlinear Schrödinger Equations," Discrete and Continuous Dynamical Systems- Series A, vol. 41, no. 3, pp. 1507 - 1517, American Institute of Mathematical Sciences (AIMS), Mar 2021.
The definitive version is available at https://doi.org/10.3934/dcds.2020328
Department(s)
Mathematics and Statistics
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
Comments
Japan Society for the Promotion of Science, Grant JP17H02854