Nonlinear scattering with nonlocal interaction

Hayato Nawa, Tohru Ozawa

Research output: Contribution to journalArticle

28 Citations (Scopus)

Abstract

We consider the scattering problem for the Hartree type equation in ℝn with n≧2: {Mathematical expression} where {Mathematical expression} and * denotes the convolution in ℝn. We prove the existence of wave operators in H0, k = {ψ∈L2(ℝn);|x|kψ∈L2(ℝn)} for any positive integer k under the assumption 1<γ1, γ2<2. This is an optimal result in the sense that the existence of wave operators breaks down if min (γ1, γ2≢1. The case where 1<γ1, γ2 = 2 is also treated according to the sign of λ2.

Original languageEnglish
Pages (from-to)259-275
Number of pages17
JournalCommunications in Mathematical Physics
Volume146
Issue number2
DOIs
Publication statusPublished - 1992 May
Externally publishedYes

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Nonlocal Interactions
Wave Operator
Scattering
operators
Scattering Problems
scattering
convolution integrals
integers
Breakdown
Convolution
breakdown
interactions
Denote
Integer

ASJC Scopus subject areas

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

Cite this

Nonlinear scattering with nonlocal interaction. / Nawa, Hayato; Ozawa, Tohru.

In: Communications in Mathematical Physics, Vol. 146, No. 2, 05.1992, p. 259-275.

Research output: Contribution to journalArticle

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