Scattering problem for the supercritical nonlinear schrödinger equation in 1d

Nakao Hayashi, Pavel I. Naumkin

Research output: Contribution to journalArticlepeer-review

Abstract

We consider the one dimensional nonlinear Schrödinger equation iut+uxx/2 =f(u),x ∈ R, t> 0,u(0,x) =u0(x),x ∈ R, with a super critical nonlinearity f(u) = ∑j≠0fj(u), and fj(u) are such thatfj(u) = λj|u|σj−juj, where λj ∈ C, σj > 3. We prove the existence of the scattering operator in the weighted Sobolev spaces.

Original languageEnglish
Pages (from-to)451-470
Number of pages20
JournalFunkcialaj Ekvacioj
Volume58
Issue number3
DOIs
Publication statusPublished - 2015 Dec 26
Externally publishedYes

Keywords

  • Asymptotic behavior in time
  • Nonlinear schrödinger
  • Power nonlinearity
  • Scattering operator

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

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