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1 December 2022 Dynamics of strongly interacting kink-antikink pairs for scalar fields on a line
Jacek Jendrej, Michał Kowalczyk, Andrew Lawrie
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Duke Math. J. 171(18): 3643-3705 (1 December 2022). DOI: 10.1215/00127094-2022-0050

Abstract

This paper concerns classical nonlinear scalar field models on the real line. If the potential is a symmetric double well, then such a model admits static solutions called kinks and antikinks, which are among the simplest examples of topological solitons. We study pure kink-antikink pairs, which are solutions that converge in one infinite time direction to a superposition of one kink and one antikink, without radiation. Our main result is a complete classification of all kink-antikink pairs in the strongly interacting regime, which means the speeds of the kinks tend asymptotically to zero. We show that up to translation there is exactly one such solution, and we give a precise description of the dynamics of the kink separation.

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Jacek Jendrej. Michał Kowalczyk. Andrew Lawrie. "Dynamics of strongly interacting kink-antikink pairs for scalar fields on a line." Duke Math. J. 171 (18) 3643 - 3705, 1 December 2022. https://doi.org/10.1215/00127094-2022-0050

Information

Received: 19 May 2020; Revised: 15 November 2021; Published: 1 December 2022
First available in Project Euclid: 18 November 2022

Digital Object Identifier: 10.1215/00127094-2022-0050

Subjects:
Primary: 35L71
Secondary: 35B40 , 37K40

Keywords: kink , large-time asymptotics , multisoliton , strong interaction

Rights: Copyright © 2022 Duke University Press

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Vol.171 • No. 18 • 1 December 2022
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