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

7 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)

Access to Document

10.1002/mma.4080

Fingerprint Dive into the research topics of 'Asymptotics for the third-order nonlinear Schrödinger equation in the critical case'. Together they form a unique fingerprint.

Cite this

@article{e33cb390183b4076857485edfb396e0f,

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.}",

year = "2017",

month = mar,

day = "30",

doi = "10.1002/mma.4080",

language = "English",

volume = "40",

pages = "1573--1597",

journal = "Mathematical Methods in the Applied Sciences",

issn = "0170-4214",

publisher = "John Wiley and Sons Ltd",

number = "5",

}

TY - JOUR

T1 - Asymptotics for the third-order nonlinear Schrödinger equation in the critical case

AU - Hayashi, Nakao

AU - Kaikina, Elena I.

PY - 2017/3/30

Y1 - 2017/3/30

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

UR - http://www.scopus.com/inward/record.url?scp=84992045321&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84992045321&partnerID=8YFLogxK

U2 - 10.1002/mma.4080

DO - 10.1002/mma.4080

M3 - Article

AN - SCOPUS:84992045321

VL - 40

SP - 1573

EP - 1597

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

SN - 0170-4214

IS - 5

ER -