Long range scattering for nonlinear Schrödinger equations in one space dimension

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159 Citations (Scopus)

Abstract

We consider the scattering problem for the nonlinear Schrödinger equation in 1+1 dimensions:[Figure not available: see fulltext.] where ∂ = ∂/∂x, λ∈R{set minus}{0}, μ∈R, p>3. We show that modified wave operators for (*) exist on a dense set of a neighborhood of zero in the Lebesgue space L2(R) or in the Sobolev space H1(R)., The modified wave operators are introduced in order to control the long range nonlinearity λ|u|2u.

Original languageEnglish
Pages (from-to)479-493
Number of pages15
JournalCommunications in Mathematical Physics
Volume139
Issue number3
DOIs
Publication statusPublished - 1991 Aug 1

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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