Defect-mediated snaking: A new growth mechanism for localized structures

Ma, Yi-Ping, Burke, J. and Knobloch, Edgar (2010) Defect-mediated snaking: A new growth mechanism for localized structures. Physica D: Nonlinear Phenomena, 239 (19). pp. 1867-1883. ISSN 0167-2789

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Abstract

Stationary spatially localized patterns in parametrically driven systems are studied, focusing on the 2:1 and 1:1 resonance tongues as described by the forced complex Ginzburg–Landau equation. Homoclinic snaking is identified in both cases and the nature of the growth of the localized structures along the snaking branches is described. The structures grow from a central defect that inserts new rolls on either side, while pushing existing rolls outwards. This growth mechanism differs fundamentally from that found in other systems exhibiting homoclinic snaking in which new rolls are added at the fronts that connect the structure to the background homogeneous state.

Item Type:	Article
Uncontrolled Keywords:	Localized states; Spatial dynamics; Homoclinic snaking; Forced complex Ginzburg–Landau equation
Subjects:	F300 Physics G100 Mathematics
Department:	Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Depositing User:	Dr Yi-Ping Ma
Date Deposited:	24 Nov 2016 09:05
Last Modified:	12 Oct 2019 22:28
URI:	http://nrl.northumbria.ac.uk/id/eprint/28412

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