Long range scattering for non-linear Schrödinger and Hartree equations in space dimension n≥2

J. Ginibre, Tohru Ozawa

Research output: Contribution to journalArticle

111 Citations (Scopus)

Abstract

We consider the scattering problem for the non-linear Schrödinger (NLS) equation with a power interaction with critical power p=1+2/n in space dimensions n=2 and 3 and for the Hartree equation with potential |x|-1 in space dimension n≥2. We prove the existence of modified wave operators in the L2 sense on a dense set of small and sufficiently regular asymptotic states.

Original languageEnglish
Pages (from-to)619-645
Number of pages27
JournalCommunications in Mathematical Physics
Volume151
Issue number3
DOIs
Publication statusPublished - 1993 Feb
Externally publishedYes

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Hartree Equation
Nonlinear Equations
Scattering
Wave Operator
Scattering Problems
scattering
Range of data
nonlinear equations
operators
Interaction
interactions

ASJC Scopus subject areas

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

Cite this

Long range scattering for non-linear Schrödinger and Hartree equations in space dimension n≥2. / Ginibre, J.; Ozawa, Tohru.

In: Communications in Mathematical Physics, Vol. 151, No. 3, 02.1993, p. 619-645.

Research output: Contribution to journalArticle

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