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

Nakao Hayashi; Elena I. Kaikina

doi:10.1002/mma.4080

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

Nakao Hayashi, Elena I. Kaikina

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

10 Citations (Scopus)

Abstract

We consider the Cauchy problem for the third-order nonlinear Schrödinger equation where H = F^-1 iξ ǀξǀ^-1 F and F is the Fourier transform. Our purpose in this paper is to prove the large time asymptoitic behavior of solutions for the defocusing case λ > 0 with a logarithmic correction under the non zero mass condition ∫u₀ (x) dx ≠ 0

Original language	English
Pages (from-to)	1573-1597
Number of pages	25
Journal	Mathematical Methods in the Applied Sciences
Volume	40
Issue number	5
DOIs	https://doi.org/10.1002/mma.4080
Publication status	Published - 2017 Mar 30
Externally published	Yes

Keywords

Third-order nonlinear Schrödinger equation
large time asymptotics

ASJC Scopus subject areas

Mathematics(all)
Engineering(all)

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10.1002/mma.4080

Cite this

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title = "Asymptotics for the third-order nonlinear Schr{\"o}dinger equation in the critical case",

abstract = "We consider the Cauchy problem for the third-order nonlinear Schr{\"o}dinger equation where H = F-1 iξ ǀξǀ-1 F and F is the Fourier transform. Our purpose in this paper is to prove the large time asymptoitic behavior of solutions for the defocusing case λ > 0 with a logarithmic correction under the non zero mass condition ∫u0 (x) dx ≠ 0",

keywords = "Third-order nonlinear Schr{\"o}dinger equation, large time asymptotics",

author = "Nakao Hayashi and Kaikina, {Elena I.}",

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AU - Kaikina, Elena I.

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N2 - We consider the Cauchy problem for the third-order nonlinear Schrödinger equation where H = F-1 iξ ǀξǀ-1 F and F is the Fourier transform. Our purpose in this paper is to prove the large time asymptoitic behavior of solutions for the defocusing case λ > 0 with a logarithmic correction under the non zero mass condition ∫u0 (x) dx ≠ 0

AB - We consider the Cauchy problem for the third-order nonlinear Schrödinger equation where H = F-1 iξ ǀξǀ-1 F and F is the Fourier transform. Our purpose in this paper is to prove the large time asymptoitic behavior of solutions for the defocusing case λ > 0 with a logarithmic correction under the non zero mass condition ∫u0 (x) dx ≠ 0

KW - Third-order nonlinear Schrödinger equation

KW - large time asymptotics

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ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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