Factorization technique for the fourth-order nonlinear Schrödinger equation

Nakao Hayashi, Pavel I. Naumkin

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)

Abstract

We consider the Cauchy problem for the cubic fourth-order nonlinear Schrödinger equation (Formula Presented),where λ∈R. We introduce the factorization formula for the free evolution group to prove the global existence of solutions. Also we show that the large time asymptotics of solutions has a logarithmic correction in the phase comparing with the corresponding linear case.

Original languageEnglish
Pages (from-to)2343-2377
Number of pages35
JournalZeitschrift fur Angewandte Mathematik und Physik
Volume66
Issue number5
DOIs
Publication statusPublished - 2015 Oct 1
Externally publishedYes

Keywords

  • Critical order of nonlinearity
  • Factorization formula
  • Fourth-order nonlinear Schrödinger equation
  • Large time asymptotics of solutions
  • Logarithmic phase correction

ASJC Scopus subject areas

  • Mathematics(all)
  • Physics and Astronomy(all)
  • Applied Mathematics

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