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The eikonal approximation to excitable reaction-diffusion systems: travelling non-planar wave fronts on the plane

Mulholland, A.J. and Gomatam, J. (1996) The eikonal approximation to excitable reaction-diffusion systems: travelling non-planar wave fronts on the plane. Physica D: Nonlinear Phenomena, 89 (3-4). pp. 329-345. ISSN 0167-2789

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Abstract

Exact, non-planar travelling solutions of the eikonal equation on an infinite plane are presented for the first time. These solutions are matched to produce corrugated wave fronts and patterns such as 'spot' solutions as well as extended parabolic type wave fronts. The stability of these solutions is also analysed. The variational equation which belongs to a generalised Wangerin class of differential equations is solved, first with the aid of the Liouville-Green approximation for the estimated eigenvalues characterising stability and then by a more elaborate shooting-matching method. All of the three types of travelling solutions are found to be geometrically stable. It is suggested that some of these predictions are experimentally testable.

Item type: Article
ID code: 18663
Keywords: Mathematics, Statistical and Nonlinear Physics, Condensed Matter Physics
Subjects: Science > Mathematics
Department: Faculty of Science > Mathematics and Statistics
Related URLs:
    Depositing user: Mrs Carolynne Westwood
    Date Deposited: 15 Oct 2010 13:55
    Last modified: 05 Sep 2014 00:51
    URI: http://strathprints.strath.ac.uk/id/eprint/18663

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