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Nonlinear Sciences > Pattern Formation and Solitons

arXiv:1404.5824 (nlin)
[Submitted on 23 Apr 2014]

Title:Analyzing critical propagation in a reaction-diffusion-advection model using unstable slow waves

Authors:Frederike Kneer, Klaus Obermayer, Markus A. Dahlem
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Abstract:The effect of advection on the critical minimal speed of traveling waves is studied. Previous theoretical studies estimated the effect on the velocity of stable fast waves and predicted the existence of a critical advection strength below which propagating waves are not supported anymore. In this paper, the critical advection strength is calculated taking into account the unstable slow wave solution. Thereby, theoretical results predict, that advection can induce stable wave propagation in the non-excitable parameter regime, if the advection strength exceeds a critical value. In addition, an analytical expression for the advection-velocity relation of the unstable slow wave is derived. Predictions are confirmed numerically in a two-variable reaction-diffusion model.
Comments: 11 pages, 8 figures
Subjects: Pattern Formation and Solitons (nlin.PS)
Cite as: arXiv:1404.5824 [nlin.PS]
  (or arXiv:1404.5824v1 [nlin.PS] for this version)
  https://doi.org/10.48550/arXiv.1404.5824

Submission history

From: Markus Dahlem [view email]
[v1] Wed, 23 Apr 2014 13:54:15 UTC (155 KB)
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