Running tails as codimension two quasi-solitons in excitation taxis waves with negative refractoriness

M. A. Tsyganov, G. R. Ivanitsky, V. N. Biktashev

Submitted to CSF 2007/06/26. Accepted 2007/10/08. Published online 2007/11/26. DOI:10.1016/j.chaos.2007.10.014 . Printed CSF 40: 2271-2276, 2009/05/15

We describe a new type of wave phenomena observed in reaction-taxis systems of equations. This is ``running tail'', a localized stable perturbation steadily moving laterally along the back of a plane wave. This phenomenon is related to ``negative refractoriness'', a property observed in some excitable systems with cross-diffusion instead of usual diffusion. We suggest a simple mechanism of such running tails for the Keller-Segel model describing chemotaxis of bacteria on the nutrient substrate. We also demonstrate that collision of running tails may happen by ``quasi-soliton'' and ``half-soliton'' scenarios.