Burke, J., Houghton, S.M. and Knobloch, E. (2009) Swift-Hohenberg equation with broken reflection symmetry. Physical Review E, 80 (3). 036202-1. ISSN 1539-3755
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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | This article has been accepted for publication in 'Physical Review E'. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Swift-Hohenberg equation, Symmetry breaking |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Funding Information: | Funder Grant number EPSRC EP/D032334/1 NSF DMS-0605238 |
Depositing User: | Dr S M Houghton |
Date Deposited: | 17 Sep 2009 09:29 |
Last Modified: | 10 Nov 2015 10:58 |
Published Version: | http://dx.doi.org/10.1103/PhysRevE.80.036202 |
Status: | Published |
Publisher: | American Physical Society |
Refereed: | Yes |
Identification Number: | 10.1103/PhysRevE.80.036202 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:9293 |