Global existence of small solutions to the quadratic nonlinear Schrödinger equations in two space dimensions

Nakao Hayashi, Pavel I. Naumkin

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

We study a global existence in time of small solutions to the quadratic nonlinear Schrödinger equation in two space dimensions, (formula presented) where (formula presented) λjk, μjk ∈ C. We prove that if the initial data u0 satisfy some analyticity and smallness conditions in a suitable norm, then the solution of the Cauchy problem (0.1) exists globally in time. Furthermore we prove the existence of the usual scattering states.

Original languageEnglish
Pages (from-to)1390-1403
Number of pages14
JournalSIAM Journal on Mathematical Analysis
Volume32
Issue number6
DOIs
Publication statusPublished - 2001 Feb 1
Externally publishedYes

Keywords

  • Global existence
  • Nonlinear Schrödinger equations
  • Quadratic nonlinearities
  • Two spatial dimensions

ASJC Scopus subject areas

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

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