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

J. Ginibre, Tohru Ozawa

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115 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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ASJC Scopus subject areas

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

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