Large time asymptotics for the fourth-order nonlinear Schrödinger equation

Nakao Hayashi, Pavel I. Naumkin

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)

Abstract

We consider the Cauchy problem for the fourth-order nonlinear Schrödinger equation in the super critical case i∂tu+14∂x4u=λ∂x(|u|ρ-1u), where ρ. >. 4, λ. ∈. C. We prove the global existence and the large time asymptotics of solutions for small initial data u0∈H1∩H12,1, when the order of the nonlinearity ρ. >. 4.

Original languageEnglish
Pages (from-to)880-905
Number of pages26
JournalJournal of Differential Equations
Volume258
Issue number3
DOIs
Publication statusPublished - 2015 Feb 1
Externally publishedYes

Keywords

  • Fourth-order nonlinear Schrödinger equation
  • Large time asymptotics

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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