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Swift-Hohenberg equation with broken reflection symmetry

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

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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: 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
Institution: The University of Leeds
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: 17 Sep 2009 09:29
Last Modified: 08 Feb 2013 16:59
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
URI: http://eprints.whiterose.ac.uk/id/eprint/9293

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