Pushed and pulled fronts in a discrete reaction-diffusion equation
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...
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| Format: | Article |
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Springer
2015
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| Online Access: | https://eprints.nottingham.ac.uk/30687/ |
| _version_ | 1848794038499540992 |
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| author | King, John R. O'Dea, Reuben D. |
| author_facet | King, John R. O'Dea, Reuben D. |
| author_sort | King, John R. |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T19:09:50Z |
| format | Article |
| id | nottingham-30687 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:09:50Z |
| publishDate | 2015 |
| publisher | Springer |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-306872020-05-04T17:23:58Z https://eprints.nottingham.ac.uk/30687/ Pushed and pulled fronts in a discrete reaction-diffusion equation King, John R. O'Dea, Reuben D. 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. Springer 2015-11-07 Article PeerReviewed 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 Discrete Reaction-Diffusion Equation Liouville-Green Matched-Asymptotic Analysis Travelling Waves http://link.springer.com/article/10.1007/s10665-015-9829-3 doi:10.1007/s10665-015-9829-3 doi:10.1007/s10665-015-9829-3 |
| spellingShingle | Discrete Reaction-Diffusion Equation Liouville-Green Matched-Asymptotic Analysis Travelling Waves King, John R. O'Dea, Reuben D. Pushed and pulled fronts in a discrete reaction-diffusion equation |
| title | Pushed and pulled fronts in a discrete reaction-diffusion equation |
| title_full | Pushed and pulled fronts in a discrete reaction-diffusion equation |
| title_fullStr | Pushed and pulled fronts in a discrete reaction-diffusion equation |
| title_full_unstemmed | Pushed and pulled fronts in a discrete reaction-diffusion equation |
| title_short | Pushed and pulled fronts in a discrete reaction-diffusion equation |
| title_sort | pushed and pulled fronts in a discrete reaction-diffusion equation |
| topic | Discrete Reaction-Diffusion Equation Liouville-Green Matched-Asymptotic Analysis Travelling Waves |
| url | https://eprints.nottingham.ac.uk/30687/ https://eprints.nottingham.ac.uk/30687/ https://eprints.nottingham.ac.uk/30687/ |