Journal of the Mathematical Society of Japan

Global dynamics below excited solitons for the nonlinear Schrödinger equation with a potential

Kenji NAKANISHI

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Abstract

Consider the nonlinear Schrödinger equation (NLS) with a potential with a single negative eigenvalue. It has solitons with negative small energy, which are asymptotically stable, and, if the nonlinearity is focusing, then also solitons with positive large energy, which are unstable. In this paper we classify the global dynamics below the second lowest energy of solitons under small mass and radial symmetry constraints.

Article information

Source
J. Math. Soc. Japan, Volume 69, Number 4 (2017), 1353-1401.

Dates
First available in Project Euclid: 25 October 2017

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1508918561

Digital Object Identifier
doi:10.2969/jmsj/06941353

Mathematical Reviews number (MathSciNet)
MR3715808

Zentralblatt MATH identifier
1383.35213

Subjects
Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]

Keywords
nonlinear Schrödinger equation scattering theory solitons blow-up

Citation

NAKANISHI, Kenji. Global dynamics below excited solitons for the nonlinear Schrödinger equation with a potential. J. Math. Soc. Japan 69 (2017), no. 4, 1353--1401. doi:10.2969/jmsj/06941353. https://projecteuclid.org/euclid.jmsj/1508918561


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