Pushed and pulled fronts in a discrete reaction-diffusion equation

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King, John R. and O'Dea, Reuben D. (2015) Pushed and pulled fronts in a discrete reaction-diffusion equation. Journal of Engineering Mathematics . pp. 1-28. ISSN 1573-2703

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Abstract

We consider the propagation of wave fronts connecting unstable and stable uniform solutions to a discrete reaction-diffusion equation on a one-dimensional integer lattice. The dependence of the wavespeed on the coupling strength µ between lattice points and on a detuning parameter (α) appearing in a nonlinear forcing is investigated thoroughly. Via asymptotic and numerical studies, the speed both of 'pulled' fronts (whereby the wavespeed can be characterised by the linear behaviour at the leading edge of the wave) and of 'pushed' fronts (for which the nonlinear dynamics of the entire front determine the wavespeed) is investigated in detail. The asymptotic and numerical techniques employed complement each other in highlighting the transition between pushed and pulled fronts under variations of µ and α.

Item Type: Article
RIS ID: https://nottingham-repository.worktribe.com/output/767313
Additional Information: The final publication is available at Springer via http://dx.doi.org/10.1007/s10665-015-9829-3
Keywords: Discrete Reaction-Diffusion Equation, Liouville-Green, Matched-Asymptotic Analysis, Travelling Waves
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Identification Number: 10.1007/s10665-015-9829-3
Depositing User: O'Dea, Dr Reuben
Date Deposited: 10 Nov 2015 09:32
Last Modified: 04 May 2020 17:23
URI: https://eprints.nottingham.ac.uk/id/eprint/30687

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