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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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.
|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:||10 Nov 2015 10:58|
|Publisher:||American Physical Society|
Available Versions of this Item
Swift-Hohenberg equation with broken reflection symmetry. (deposited 13 Aug 2009 14:49)
- Swift-Hohenberg equation with broken reflection symmetry. (deposited 17 Sep 2009 09:29) [Currently Displayed]