Failure of Scattering to Solitary Waves for Long-Range Nonlinear Schrödinger Equations
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.
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
Mathematics and Statistics
Keywords and Phrases
Failure of scattering; Long-range nonlinearities; Nonlinear Schrödinger equations
International Standard Serial Number (ISSN)
Article - Journal
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01 Mar 2021