Modulation theory for radially symmetric kink waves governed by a multi-dimensional sine-Gordon equation

Nguyen, L. T. K. and Smyth, N. F. (2023) Modulation theory for radially symmetric kink waves governed by a multi-dimensional sine-Gordon equation. Journal of Nonlinear Science, 33(1), 11. (doi: 10.1007/s00332-022-09859-w)

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Abstract

We derive a modulation theory for the resolution of radially symmetric kink waves governed by a multi-dimensional sine-Gordon equation. Whitham modulation theory is developed to explain the return of an expanding kink wave, as well as predicting its maximum expansion radius and its return time. Comparisons with full numerical solutions of the sine-Gordon equation show that the modulation theory gives excellent predictions for not only the returning time and the maximum expansion radius, but also for the details of the kink itself. In addition, the method can be extended to dissipative sine-Gordon equations and generalized to deal with a wide class of initial conditions beyond kinks.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Nguyen, Dr Khiem
Authors: Nguyen, L. T. K., and Smyth, N. F.
College/School:College of Science and Engineering > School of Engineering > Systems Power and Energy
Journal Name:Journal of Nonlinear Science
Publisher:Springer
ISSN:0938-8974
ISSN (Online):1432-1467
Published Online:19 November 2022
Copyright Holders:Copyright © 2022 The Authors
First Published:First published in Journal of Nonlinear Science 33(1): 11
Publisher Policy:Reproduced under a Creative Commons License

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