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Sine-Gordon on a wormhole

Published version
Peer-reviewed

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Authors

Bizoń, Piotr 
Dunajski, Maciej 
Kahl, Michał 
Kowalczyk, Michał 

Abstract

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 one-kink using the Soffer–Weinstein weakly nonlinear perturbation theory.

Description

Keywords

Paper, soliton resolution conjecture, asymptotic stability of solitons, nonlinear dispersive equations, 35C08

Journal Title

Nonlinearity

Conference Name

Journal ISSN

0951-7715
1361-6544

Volume Title

34

Publisher

IOP Publishing
Sponsorship
Comisión Nacional de Investigación Científica y Tecnológica (PIA AFB170001)
Science and Technology Facilities Council (ST/P000681/1)
Fondo Nacional de Desarrollo Científico y Tecnológico (1170164)
Narodowe Centrum Nauki (2017/26/A/ST2/00530)