Factorization technique for the fourth-order nonlinear Schrödinger equation

Nakao Hayashi; Pavel I. Naumkin

doi:10.1007/s00033-015-0524-z

Factorization technique for the fourth-order nonlinear Schrödinger equation

Nakao Hayashi, Pavel I. Naumkin

Research output: Contribution to journal › Article › peer-review

18 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 language	English
Pages (from-to)	2343-2377
Number of pages	35
Journal	Zeitschrift fur Angewandte Mathematik und Physik
Volume	66
Issue number	5
DOIs	https://doi.org/10.1007/s00033-015-0524-z
Publication status	Published - 2015 Oct 1
Externally published	Yes

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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10.1007/s00033-015-0524-z

Cite this

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abstract = "We consider the Cauchy problem for the cubic fourth-order nonlinear Schr{\"o}dinger 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.",

keywords = "Critical order of nonlinearity, Factorization formula, Fourth-order nonlinear Schr{\"o}dinger equation, Large time asymptotics of solutions, Logarithmic phase correction",

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language = "English",

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AU - Naumkin, Pavel I.

PY - 2015/10/1

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AB - 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.

KW - Critical order of nonlinearity

KW - Factorization formula

KW - Fourth-order nonlinear Schrödinger equation

KW - Large time asymptotics of solutions

KW - Logarithmic phase correction

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ER -

Factorization technique for the fourth-order nonlinear Schrödinger equation

Abstract

Keywords

ASJC Scopus subject areas

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