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Homoclinic snaking in bounded domains

Houghton, S.M. and Knobloch, E. (2009) Homoclinic snaking in bounded domains. Physical Review E, 80 (2). 026210. ISSN 1539-3755


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Homoclinic snaking is a term used to describe the back and forth oscillation of a branch of time-independent spatially localized states in a bistable, spatially reversible system as the localized structure grows in length by repeatedly adding rolls on either side. On the real line this process continues forever. In finite domains snaking terminates once the domain is filled but the details of how this occurs depend critically on the choice of boundary conditions. With periodic boundary conditions the snaking branches terminate on a branch of spatially periodic states. However, with non-Neumann boundary conditions they turn continuously into a large amplitude filling state that replaces the periodic state. This behavior, shown here in detail for the Swift-Hohenberg equation, explains the phenomenon of “snaking without bistability”, recently observed in simulations of binary fluid convection by Mercader, Batiste, Alonso and Knobloch (preprint).

Item Type: Article
Copyright, Publisher and Additional Information: This is an author produced version of a paper accepted for publication in "Physical Review E". Uploaded in accordance with the publisher's self-archiving policy.
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)
Funding Information:
FunderGrant number
Depositing User: Dr S M Houghton
Date Deposited: 03 Jul 2009 14:48
Last Modified: 08 Feb 2013 16:58
Published Version: http://dx.doi.org/10.1103/PhysRevE.80.026210
Status: Published
Publisher: American Physical Society
Refereed: Yes
Identification Number: 10.1103/PhysRevE.80.026210
URI: http://eprints.whiterose.ac.uk/id/eprint/8749

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