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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Official URL: http://dx.doi.org/10.1007/s10884-010-9195-9
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.
|Additional Information:||The original publication is available at http://www.springerlink.com|
|Divisions:||Faculty of Engineering and Physical Sciences > Mathematics|
|Deposited By:||Symplectic Elements|
|Deposited On:||13 Jun 2012 12:42|
|Last Modified:||08 Jun 2013 15:21|
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