Scattering for the L2supercritical point NLS

Riccardo Adami, Reika Fukuizumi, Justin Holmer

研究成果: Article査読

3 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)35-60
ページ数26
ジャーナルTransactions of the American Mathematical Society
374
1
DOI
出版ステータスPublished - 2020

ASJC Scopus subject areas

  • 数学 (全般)
  • 応用数学

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