Nonlinear instability of linearly unstable standing waves for nonlinear Schrödinger equations

Vladimir Georgiev; Masahito Ohta

doi:10.2969/jmsj/06420533

Nonlinear instability of linearly unstable standing waves for nonlinear Schrödinger equations

Vladimir Georgiev^*, Masahito Ohta

^*この研究の対応する著者

研究成果: Article › 査読

20 被引用数 (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.

本文言語	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
巻	64
号	2
DOI	https://doi.org/10.2969/jmsj/06420533
出版ステータス	Published - 2012
外部発表	はい

ASJC Scopus subject areas

数学 (全般)

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10.2969/jmsj/06420533

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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 = "Vladimir Georgiev 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",

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

AU - Georgiev, Vladimir

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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U2 - 10.2969/jmsj/06420533

DO - 10.2969/jmsj/06420533

M3 - Article

AN - SCOPUS:84866889844

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VL - 64

SP - 533

EP - 548

JO - Journal of the Mathematical Society of Japan

JF - Journal of the Mathematical Society of Japan

IS - 2

ER -

Nonlinear instability of linearly unstable standing waves for nonlinear Schrödinger equations

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