Modified wave operators for nonlinear Schrödinger equations in lower order Sobolev spaces

Nakao Hayashi, Huimei Wang, Pavel I. Naumkin

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)

Abstract

We study the final value problem for the nonlinear Schrödinger equations in one or two space dimensions with the gauge-invariant nonlinearity of the critical long-range power and nonresonant polynomial nonlinearities of the same power, which are not gauge invariant. We construct a unique global solution (for positive time) which is asymptotic for large time to a given profile with sufficiently small norm in lower order Sobolev spaces with decay at the spatial infinity and at the zero frequency.

Original languageEnglish
Pages (from-to)759-775
Number of pages17
JournalJournal of Hyperbolic Differential Equations
Volume8
Issue number4
DOIs
Publication statusPublished - 2011 Dec

Keywords

  • Modified wave operators
  • lower order Sobolev
  • nonlinear Schrödinger equations

ASJC Scopus subject areas

  • Analysis
  • Mathematics(all)

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