Modified wave operators for nonlinear Schrödinger equations in one and two dimensions

Nakao Hayashi, Pavel I. Naumkin, Akihiro Shimomura, Satoshi Tonegawa

Research output: Contribution to journalArticlepeer-review

29 Citations (Scopus)

Abstract

We study the asymptotic behavior of solutions, in particular the scattering theory, for the nonlinear Schrödinger equations with cubic and quadratic nonlinearities in one or two space dimensions. The nonlinearities are summation of gauge invariant term and non-gauge invariant terms. The scattering problem of these equations belongs to the long range case. We prove the existence of the modified wave operators to those equations for small final data. Our result is an improvement of the previous work [13].

Original languageEnglish
Pages (from-to)1-16
Number of pages16
JournalElectronic Journal of Differential Equations
Volume2004
Publication statusPublished - 2004 Apr 21
Externally publishedYes

Keywords

  • Modified wave operators
  • Nonlinear Schrödinger equations

ASJC Scopus subject areas

  • Analysis

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