Journal of the Mathematical Society of Japan

Nonlinear instability of linearly unstable standing waves for nonlinear Schrödinger equations

Vladimir GEORGIEV and Masahito OHTA

Full-text: Open access

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.

Article information

Source
J. Math. Soc. Japan, Volume 64, Number 2 (2012), 533-548.

Dates
First available in Project Euclid: 26 April 2012

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1335444402

Digital Object Identifier
doi:10.2969/jmsj/06420533

Mathematical Reviews number (MathSciNet)
MR2916078

Zentralblatt MATH identifier
1253.35158

Subjects
Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]
Secondary: 35B35: Stability 35B45: A priori estimates

Keywords
nonlinear Schrodinger equation standing wave instability Strichartz estimate

Citation

GEORGIEV, Vladimir; OHTA, Masahito. Nonlinear instability of linearly unstable standing waves for nonlinear Schrödinger equations. J. Math. Soc. Japan 64 (2012), no. 2, 533--548. doi:10.2969/jmsj/06420533. https://projecteuclid.org/euclid.jmsj/1335444402


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