Low energy scattering for nonlinear Schrödinger equations in fractional order Sobolev spaces

M. Nakamura, T. Ozawa

Research output: Contribution to journalArticle

34 Citations (Scopus)

Abstract

We consider the scattering problem for the nonlinear Schrödinger equations with interactions behaving as a power p at zero. In the critical and subcritical cases (s ≥ n/2-2/(p-1) ≥ 0), we prove the existence and asymptotic completeness of wave operators in the sense of Sobolev norm of order s on a set of asymptotic states with small homogeneous norm of order n/2-2/(p-1) in space dimension n ≥ 1.

Original languageEnglish
Pages (from-to)397-410
Number of pages14
JournalReviews in Mathematical Physics
Volume9
Issue number3
DOIs
Publication statusPublished - 1997 Apr
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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