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Decay of bound states in a sine-Gordon equation with double well potentials

Ali, Amir; Susanto, Hadi; Wattis, Jonathan A.D.

Authors

Amir Ali

Hadi Susanto

JONATHAN WATTIS jonathan.wattis@nottingham.ac.uk
Professor of Applied Mathematics



Abstract

We consider a spatially inhomogeneous sine-Gordon equation with a double-well potential, describing long Josephson junctions with phase-shifts. We discuss the interactions of symmetric and antisymmetric bound states in the system. Using a multiple scale expansion, we show that the modes decay algebraically in time due to the energy transfer from the discrete to the continuous spectrum. In particular, exciting the two modes at the same time yields an increased decay rate. An external time-periodic drive is shown to sustain symmetric state, while it damps the antisymmetric one.

Citation

Ali, A., Susanto, H., & Wattis, J. A. (2015). Decay of bound states in a sine-Gordon equation with double well potentials. Journal of Mathematical Physics, 56, Article 051502. https://doi.org/10.1063/1.4917284

Journal Article Type Article
Publication Date Jan 1, 2015
Deposit Date Nov 12, 2015
Publicly Available Date Mar 28, 2024
Journal Journal of Mathematical Physics
Print ISSN 0022-2488
Electronic ISSN 1089-7658
Publisher American Institute of Physics
Peer Reviewed Peer Reviewed
Volume 56
Article Number 051502
DOI https://doi.org/10.1063/1.4917284
Public URL https://nottingham-repository.worktribe.com/output/987607
Publisher URL http://scitation.aip.org/content/aip/journal/jmp/56/5/10.1063/1.4917284
Additional Information Copyright 2015 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in G. A. Gibson et al., Journal of Mathematical Physics 56, 051502 (2015) http://dx.doi.org/10.1063/1.4917284 and may be found at http://scitation.aip.org/content/aip/journal/jmp/56/5/10.1063/1.4917284.

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