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

^*Corresponding author for this work

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

20 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	533-548
Number of pages	16
Journal	Journal of the Mathematical Society of Japan
Volume	64
Issue number	2
DOIs	https://doi.org/10.2969/jmsj/06420533
Publication status	Published - 2012
Externally published	Yes

Keywords

Instability
Nonlinear Schrödinger equation
Standing wave
Strichartz estimate

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.2969/jmsj/06420533

Cite this

@article{30fd89026ef94a9bb57da0f775cb697b,

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",

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 - 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

UR - http://www.scopus.com/inward/record.url?scp=84866889844&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84866889844&partnerID=8YFLogxK

U2 - 10.2969/jmsj/06420533

DO - 10.2969/jmsj/06420533

M3 - Article

AN - SCOPUS:84866889844

SN - 0025-5645

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

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this