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

M. Nakamura, Tohru Ozawa

Research output: Contribution to journalArticle

33 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
Publication statusPublished - 1997 Apr
Externally publishedYes

Fingerprint

Sobolev space
Fractional Order
norms
Sobolev Spaces
nonlinear equations
Nonlinear Equations
Scattering
Norm
Wave Operator
Scattering Problems
completeness
Energy
scattering
Completeness
operators
energy
Zero
Interaction
interactions

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics

Cite this

Low energy scattering for nonlinear Schrödinger equations in fractional order Sobolev spaces. / Nakamura, M.; Ozawa, Tohru.

In: Reviews in Mathematical Physics, Vol. 9, No. 3, 04.1997, p. 397-410.

Research output: Contribution to journalArticle

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