Burke, J., Houghton, S.M. and Knobloch, E. (2009) Swift-Hohenberg equation with broken reflection symmetry. Physical Review E. ISSN 1539-3755 (In Press)
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Abstract
The bistable Swift-Hohenberg equation possesses a variety of time-independent spatially localized solutions organized in the so-called snakes-and-ladders structure. This structure is a consequence of a phenomenon known as homoclinic snaking, and is in turn a consequence of spatial reversibility of the equation. We examine here the consequences of breaking spatial reversibility on the snakes-and-ladders structure. We find that the localized states now drift, and show that the snakes-and-ladders structure breaks up into a stack of isolas. We explore the evolution of this new structure with increasing reversibility breaking and study the dynamics of the system outside of the snaking region using a combination of numerical and analytical techniques.
| Item Type: | Article |
|---|---|
| Copyright, Publisher and Additional Information: | Accepted for publication in 'Physical Review E'. Uploaded in accordance with the publisher's self-archiving policy. |
| Keywords: | Swift-Hohenberg equation; Symmetry breaking |
| Academic Units: | The University of Leeds > Faculty of Maths and Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
| Depositing User: | Dr S M Houghton |
| Date Deposited: | 13 Aug 2009 14:49 |
| Last Modified: | 08 Feb 2013 16:58 |
| Status: | In Press |
| Publisher: | American Physical Society |
| Refereed: | Yes |
| URI: | http://eprints.whiterose.ac.uk/id/eprint/9120 |
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- Swift-Hohenberg equation with broken reflection symmetry. (deposited 13 Aug 2009 14:49) [Currently Displayed]
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