Asymptotics for the fourth-order nonlinear Schrödinger equation in the critical case

Nakao Hayashi, Jesus A. Mendez-Navarro, Pavel I. Naumkin

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

We consider the Cauchy problem for the fourth-order nonlinear Schrödinger equation{i∂tu−14∂x4u=λ|u|4u, (t,x)∈R+×R,u(0,x)=u0(x), x∈R. We prove the large time asymptotic behavior of solutions with a logarithmic correction under the conditions ∫u0(x)dx≠0, λ>0.

Original languageEnglish
Pages (from-to)5144-5179
Number of pages36
JournalJournal of Differential Equations
Volume261
Issue number9
DOIs
Publication statusPublished - 2016 Nov 5
Externally publishedYes

Keywords

  • Fourth-order nonlinear Schrödinger equation
  • Large time asymptotics

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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