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Isolas of 2-Pulse Solutions in Homoclinic Snaking Scenarios

Knobloch, J, Lloyd, DJB, Sandstede, B and Wagenknecht, T (2010) Isolas of 2-Pulse Solutions in Homoclinic Snaking Scenarios Journal of Dynamics and Differential Equations, 23 (1). 93 - 114. ISSN 1572-9222

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Abstract

Homoclinic snaking refers to the bifurcation structure of symmetric localised roll patterns that are often found to lie on two sinusoidal “snaking” bifurcation curves, which are connected by an infinite number of “rung” segments along which asymmetric localised rolls of various widths exist. The envelopes of all these structures have a unique maximum and we refer to them as symmetric or asymmetric 1-pulses. In this paper, the existence of stationary 1D patterns of symmetric 2-pulses that consist of two well-separated 1-pulses is established. Corroborating earlier numerical evidence, it is shown that symmetric 2-pulses exist along isolas in parameter space that are formed by parts of the snaking curves and the rungs mentioned above.

Item Type: Article
Additional Information: The original publication is available at http://www.springerlink.com
Divisions: Faculty of Engineering and Physical Sciences > Mathematics
Depositing User: Symplectic Elements
Date Deposited: 13 Jun 2012 11:42
Last Modified: 23 Sep 2013 19:18
URI: http://epubs.surrey.ac.uk/id/eprint/294640

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