Small data blow-up for a system of nonlinear Schrödinger equations

Tohru Ozawa; Hideaki Sunagawa

doi:10.1016/j.jmaa.2012.10.003

Small data blow-up for a system of nonlinear Schrödinger equations

Tohru Ozawa, Hideaki Sunagawa

先進理工学部

研究成果: Article › 査読

21 被引用数 (Scopus)

抄録

We give examples of small data blow-up for a three-component system of quadratic nonlinear Schrödinger equations in one space dimension. Our construction of the blowing-up solution is based on the Hopf-Cole transformation, which allows us to reduce the problem to getting suitable growth estimates for a solution to the transformed system. Amplification in the reduced system is shown to have a close connection with the mass resonance.

本文言語	English
ページ（範囲）	147-155
ページ数	9
ジャーナル	Journal of Mathematical Analysis and Applications
巻	399
号	1
DOI	https://doi.org/10.1016/j.jmaa.2012.10.003
出版ステータス	Published - 2013 3 1

ASJC Scopus subject areas

Analysis
Applied Mathematics

文献へのアクセス

10.1016/j.jmaa.2012.10.003

他のファイルとリンク

フィンガープリント「Small data blow-up for a system of nonlinear Schrödinger equations」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル

@article{d6f7f51a4cf44f90b846e30684e393b2,

title = "Small data blow-up for a system of nonlinear Schr{\"o}dinger equations",

abstract = "We give examples of small data blow-up for a three-component system of quadratic nonlinear Schr{\"o}dinger equations in one space dimension. Our construction of the blowing-up solution is based on the Hopf-Cole transformation, which allows us to reduce the problem to getting suitable growth estimates for a solution to the transformed system. Amplification in the reduced system is shown to have a close connection with the mass resonance.",

keywords = "Hopf-Cole transformation, Mass resonance, Nonlinear Schr{\"o}dinger equation, Small data blow-up",

author = "Tohru Ozawa and Hideaki Sunagawa",

year = "2013",

month = mar,

day = "1",

doi = "10.1016/j.jmaa.2012.10.003",

language = "English",

volume = "399",

pages = "147--155",

journal = "Journal of Mathematical Analysis and Applications",

issn = "0022-247X",

publisher = "Academic Press Inc.",

number = "1",

}

TY - JOUR

T1 - Small data blow-up for a system of nonlinear Schrödinger equations

AU - Ozawa, Tohru

AU - Sunagawa, Hideaki

PY - 2013/3/1

Y1 - 2013/3/1

N2 - We give examples of small data blow-up for a three-component system of quadratic nonlinear Schrödinger equations in one space dimension. Our construction of the blowing-up solution is based on the Hopf-Cole transformation, which allows us to reduce the problem to getting suitable growth estimates for a solution to the transformed system. Amplification in the reduced system is shown to have a close connection with the mass resonance.

AB - We give examples of small data blow-up for a three-component system of quadratic nonlinear Schrödinger equations in one space dimension. Our construction of the blowing-up solution is based on the Hopf-Cole transformation, which allows us to reduce the problem to getting suitable growth estimates for a solution to the transformed system. Amplification in the reduced system is shown to have a close connection with the mass resonance.

KW - Hopf-Cole transformation

KW - Mass resonance

KW - Nonlinear Schrödinger equation

KW - Small data blow-up

UR - http://www.scopus.com/inward/record.url?scp=84869081994&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84869081994&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2012.10.003

DO - 10.1016/j.jmaa.2012.10.003

M3 - Article

AN - SCOPUS:84869081994

VL - 399

SP - 147

EP - 155

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 1

ER -