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Defects in Oscillatory Media: Toward a Classification

Sandstede, Bjorn and Scheel, Arnd (2004) Defects in Oscillatory Media: Toward a Classification Dynamical Systems, 3. pp. 1-68.


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We investigate, in a systematic fashion, coherent structures, or defects, which serve as interfaces between wave trains with possibly different wavenumbers in reaction-diffusion systems. We propose a classification of defects into four different defect classes which have all been observed experimentally. The characteristic distinguishing these classes is the sign of the group velocities of the wave trains to either side of the defect, measured relative to the speed of the defect. Using a spatial-dynamics description in which defects correspond to homoclinic and heteroclinic connections of an ill-posed pseudoelliptic equation, we then relate robustness properties of defects to their spectral stability properties. Last, we illustrate that all four types of defects occur in the one-dimensional cubicquintic Ginzburg–Landau equation as a perturbation of the phase-slip vortex.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
Scheel, Arnd
Date : 24 February 2004
Uncontrolled Keywords : pattern formation, coherent structures, spatial dynamics, group velocity
Additional Information : Published in the SIAM Journal on Applied Dynamical Systems, 2004, Vol. 3 (1), pp. 1-68. © 2004 Society for Applied and Industrial Mathematics. Click here for the official URL.
Depositing User : Mr Adam Field
Date Deposited : 27 May 2010 14:41
Last Modified : 31 Oct 2017 14:02

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