Nonlinear instability of linearly unstable standing waves for nonlinear Schrödinger equations

Research output: Contribution to journalArticle

15 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 languageEnglish
Pages (from-to)533-548
Number of pages16
JournalJournal of the Mathematical Society of Japan
Volume64
Issue number2
DOIs
Publication statusPublished - 2012
Externally publishedYes

Fingerprint

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

Keywords

  • Instability
  • Nonlinear Schrödinger equation
  • Standing wave
  • Strichartz estimate

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Nonlinear instability of linearly unstable standing waves for nonlinear Schrödinger equations. / Gueorguiev, Vladimir Simeonov; Ohta, Masahito.

In: Journal of the Mathematical Society of Japan, Vol. 64, No. 2, 2012, p. 533-548.

Research output: Contribution to journalArticle

@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 = "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

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

VL - 64

SP - 533

EP - 548

JO - Journal of the Mathematical Society of Japan

JF - Journal of the Mathematical Society of Japan

SN - 0025-5645

IS - 2

ER -