Scattering for the L2supercritical point NLS

Riccardo Adami, Reika Fukuizumi, Justin Holmer

Research output: Contribution to journalArticlepeer-review

Abstract

We consider the 1D nonlinear Schrödinger equation with focusing point nonlinearity. "Point"means that the pure-power nonlinearity has an inhomogeneous potential and the potential is the delta function supported at the origin. This equation is used to model a Kerr-type medium with a narrow strip in the optic fibre. There are several mathematical studies on this equation and the local/global existence of a solution, blow-up occurrence, and blowup profile have been investigated. In this paper we focus on the asymptotic behavior of the global solution, i.e., we show that the global solution scatters as t → ±∞ in the L2 supercritical case. The main argument we use is due to Kenig-Merle, but it is required to make use of an appropriate function space (not Strichartz space) according to the smoothing properties of the associated integral equation.

Original languageEnglish
Pages (from-to)35-60
Number of pages26
JournalTransactions of the American Mathematical Society
Volume374
Issue number1
DOIs
Publication statusPublished - 2020

Keywords

  • Nonlinear point interaction
  • Scattering
  • Schrödinger equation

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Scattering for the L<sup>2</sup>supercritical point NLS'. Together they form a unique fingerprint.

Cite this