Exact travelling wave solutions of an “integrable” discrete reaction-diffusion equation

We construct exact travelling wave solutions of a discrete reaction-diffusion equation describing a system of coupled bistable elements. The form of the bistable potential is chosen such that in a moving frame the waveform satisfies an integrable discrete equation that can be solved explicitly. We a...

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Bibliographic Details
Published in:Physica. D 1997-08, Vol.106 (3), p.255-269
Main Authors: Bressloff, P.C., Rowlands, G.
Format: Article
Language:English
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Summary:We construct exact travelling wave solutions of a discrete reaction-diffusion equation describing a system of coupled bistable elements. The form of the bistable potential is chosen such that in a moving frame the waveform satisfies an integrable discrete equation that can be solved explicitly. We analyse the linear stability of the wave and study wave propagation failure in the weak coupling limit.
ISSN:0167-2789
1872-8022
DOI:10.1016/S0167-2789(97)00047-X