On a system of nonlinear Schrödinger equations with quadratic interaction

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Abstract

We study a system of nonlinear Schrödinger equations with quadratic interaction in space dimension n≤6. The Cauchy problem is studied in L 2, in H1, and in the weighted L2 space 〈 x〉-1L2=F(H1) under mass resonance condition, where 〈x〉=( 1+|x|2)1/2 and F is the Fourier transform. The existence of ground states is studied by variational methods. Blow-up solutions are presented in an explicit form in terms of ground states under mass resonance condition, which ensures the invariance of the system under pseudo-conformal transformations.

Original languageEnglish
Pages (from-to)661-690
Number of pages30
JournalAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume30
Issue number4
DOIs
Publication statusPublished - 2013 Jan 1

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ASJC Scopus subject areas

  • Analysis
  • Mathematical Physics
  • Applied Mathematics

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