Nonlinear instability of linearly unstable standing waves for nonlinear Schrödinger equations

研究成果: Article

15 引用 (Scopus)

抄録

We study the instability of standing waves for nonlinear Schrödinger equations. Under a general assumption on nonlinearity, we prove that linear instability implies orbital instability in any dimension. For that purpose, we establish a Strichartz type estimate for the propagator generated by the linearized operator around standing wave.

元の言語English
ページ(範囲)533-548
ページ数16
ジャーナルJournal of the Mathematical Society of Japan
64
発行部数2
DOI
出版物ステータスPublished - 2012
外部発表Yes

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Nonlinear Instability
Standing Wave
Nonlinear Equations
Linearly
Unstable
Propagator
Nonlinearity
Imply
Operator
Estimate

ASJC Scopus subject areas

  • Mathematics(all)

これを引用

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title = "Nonlinear instability of linearly unstable standing waves for nonlinear Schr{\"o}dinger equations",
abstract = "We study the instability of standing waves for nonlinear Schr{\"o}dinger equations. Under a general assumption on nonlinearity, we prove that linear instability implies orbital instability in any dimension. For that purpose, we establish a Strichartz type estimate for the propagator generated by the linearized operator around standing wave.",
keywords = "Instability, Nonlinear Schr{\"o}dinger equation, Standing wave, Strichartz estimate",
author = "Gueorguiev, {Vladimir Simeonov} and Masahito Ohta",
year = "2012",
doi = "10.2969/jmsj/06420533",
language = "English",
volume = "64",
pages = "533--548",
journal = "Journal of the Mathematical Society of Japan",
issn = "0025-5645",
publisher = "Mathematical Society of Japan - Kobe University",
number = "2",

}

TY - JOUR

T1 - Nonlinear instability of linearly unstable standing waves for nonlinear Schrödinger equations

AU - Gueorguiev, Vladimir Simeonov

AU - Ohta, Masahito

PY - 2012

Y1 - 2012

N2 - We study the instability of standing waves for nonlinear Schrödinger equations. Under a general assumption on nonlinearity, we prove that linear instability implies orbital instability in any dimension. For that purpose, we establish a Strichartz type estimate for the propagator generated by the linearized operator around standing wave.

AB - We study the instability of standing waves for nonlinear Schrödinger equations. Under a general assumption on nonlinearity, we prove that linear instability implies orbital instability in any dimension. For that purpose, we establish a Strichartz type estimate for the propagator generated by the linearized operator around standing wave.

KW - Instability

KW - Nonlinear Schrödinger equation

KW - Standing wave

KW - Strichartz estimate

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DO - 10.2969/jmsj/06420533

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JO - Journal of the Mathematical Society of Japan

JF - Journal of the Mathematical Society of Japan

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