Global existence of solutions for a subcritical nonlinear Schrödinger equation

Nakao Hayashi, Pavel I. Naumkin

Research output: Contribution to journalArticle

Abstract

We consider the one dimensional nonlinear Schrödinger equation {iut+1/2uxx=N(u,ū),x∈R,t>1,u(1,x)= u0(x),x∈R, where the nonlinearity N(u,ū)=| u|-2γu3=u3-2γū -2γ, the exponent γ>0 is sufficiently small. Our purpose in this paper is to prove a global existence in time of small solutions.

Original languageEnglish
Pages (from-to)189-213
Number of pages25
JournalNonlinear Analysis, Theory, Methods and Applications
Volume108
DOIs
Publication statusPublished - 2014 Oct

Keywords

  • Global existence
  • Nonlinear Schrödinger equation
  • Subcritical case

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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