Kink–antikink stripe interactions in the two-dimensional sine–Gordon equation

Carretero-González, R., Cisneros-Ake, L.A., Decker, R., Koutsokostas, G.N., Frantzeskakis, D.J., Kevrekidis, P.G. and Ratliff, Daniel (2022) Kink–antikink stripe interactions in the two-dimensional sine–Gordon equation. Communications in Nonlinear Science and Numerical Simulation, 109. p. 106123. ISSN 1007-5704

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Official URL: https://doi.org/10.1016/j.cnsns.2021.106123

Abstract

The main focus of the present work is to study quasi-one-dimensional kink–antikink stripes embedded in the two-dimensional sine–Gordon equation. Using variational techniques, we reduce the interaction dynamics between a kink and an antikink stripe on their respective time and space dependent widths and locations. The resulting reduced system of coupled equations is found to accurately describe the width and undulation dynamics of a single kink stripe as well as that of two interacting ones. As an aside, we also discuss two related topics: the computational identification of the kink center and its numerical implications and alternative perturbative and multiple scales approaches to the transverse direction induced dynamics for a single kink stripe in the two-dimensional realm.

Item Type: Article
Uncontrolled Keywords: Sine–Gordon equation, Kink and anti-kinks, Kink stripes, Variational approximation
Subjects: G100 Mathematics
Department: Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Depositing User: John Coen
Date Deposited: 28 Feb 2022 12:10
Last Modified: 28 Feb 2022 12:15
URI: http://nrl.northumbria.ac.uk/id/eprint/48566

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