Multichromatic travelling waves for lattice Nagumo equations

Hermen Jan Hupkes, Leonardo Morelli, Petr Stehlík and Vladimír Švígler

Applied Mathematics and Computation, 2019, vol. 361, issue C, 430-452

Abstract: We discuss multichromatic front solutions to the bistable Nagumo lattice differential equation. Such fronts connect the stable spatially homogeneous equilibria with spatially heterogeneous n-periodic equilibria and hence are not monotonic like the standard monochromatic fronts. In contrast to the bichromatic case, our results show that these multichromatic fronts can disappear and reappear as the diffusion coefficient is increased. In addition, these multichromatic waves can travel in parameter regimes where the monochromatic fronts are also free to travel. This leads to intricate collision processes where an incoming multichromatic wave can reverse its direction and turn into a monochromatic wave.

Keywords: Reaction-diffusion equations; Lattice differential equations; Travelling waves; Wave collisions (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:361:y:2019:i:c:p:430-452

DOI: 10.1016/j.amc.2019.05.036

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