Sine-Gordon on a wormhole
Authors
Bizoń, P
Dunajski, M
Kahl, M
Kowalczyk, M
Publication Date
2021Journal Title
Nonlinearity
ISSN
0951-7715
Publisher
IOP Publishing
Volume
34
Issue
8
Pages
5520-5537
Language
en
Type
Article
This Version
VoR
Metadata
Show full item recordCitation
Bizoń, P., Dunajski, M., Kahl, M., & Kowalczyk, M. (2021). Sine-Gordon on a wormhole. Nonlinearity, 34 (8), 5520-5537. https://doi.org/10.1088/1361-6544/ac08eb
Abstract
In an attempt to understand the soliton resolution conjecture, we consider
the Sine-Gordon equation on a spherically symmetric wormhole spacetime. We show
that within each topological sector (indexed by a positive integer degree $n$)
there exists a unique linearly stable soliton, which we call the $n$-kink. We
give numerical evidence that the $n$-kink is a global attractor in the
evolution of any smooth, finite energy solutions of degree $n$. When the radius
of the wormhole throat $a$ is large enough, the convergence to the $n$-kink is
shown to be governed by internal modes that slowly decay due to the resonant
transfer of energy to radiation. We compute the exact asymptotics of this
relaxation process for the $1$-kink using the Soffer-Weinstein weakly nonlinear
perturbation theory.
Keywords
Paper, soliton resolution conjecture, asymptotic stability of solitons, nonlinear dispersive equations, 35C08
Sponsorship
Science and Technology Facilities Council (ST/P000681/1)
STFC (ST/T000694/1)
Identifiers
nonac08eb, ac08eb, non-105060.r1
External DOI: https://doi.org/10.1088/1361-6544/ac08eb
This record's URL: https://www.repository.cam.ac.uk/handle/1810/332099
Rights
Licence:
https://creativecommons.org/licenses/by/3.0/
Statistics
Total file downloads (since January 2020). For more information on metrics see the
IRUS guide.