Waves in systems with cross-diffusion as a new class of nonlinear waves

M.A. Tsyganov^a, V.N. Biktashev^b, J. Brindli^c, A.V. Holden^d, G.R. Ivanitskii^a
^aInstitute for Theoretical and Experimental Biophysics, Russian Academy of Sciences, Institutskaya str. 3, Pushchino, Moscow Region, 142290, Russian Federation
^bDepartment of Mathematical Sciences, University of Liverpool, Liverpool, UK
^cDepartment of Applied Mathematics, University of Leeds, Leeds, UK
^dFaculty of Biological Sciences, University of Leeds, Leeds, UK

Research on spatially extended excitable systems with cross-diffusion components is reviewed. Particular attention is given to the new phenomena of the quasi-soliton and half-soliton interaction of excitation waves, which are specific to such systems and occur along with the standard nonsoliton wave interaction that causes the waves to mutually annihilate. A correlation is shown to exist between interaction regimes and wave profile shapes. One example of a cross-diffusion system is population systems with taxes. Based on the mathematical models of and experimental work with bacterial populations, waves in excitable cross-diffusion systems can be identified as a new class of nonlinear waves.

PACS: 05.45.−a, 87.18.Hf, 87.23.Cc (all)
DOI: 10.1070/PU2007v050n03ABEH006114
URL: https://ufn.ru/en/articles/2007/3/b/
Web of Science

000248004300002
Scopus

2-s2.0-34547251534
ADS NASA

2007PhyU...50..263T
Citation: Tsyganov M A, Biktashev V N, Brindli J, Holden A V, Ivanitskii G R "Waves in systems with cross-diffusion as a new class of nonlinear waves" Phys. Usp. 50 263–286 (2007)

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Оригинал: Цыганов М А, Бикташев В Н, Бриндли Дж, Холден А В, Иваницкий Г Р «Волны в кросс-диффузионных системах — особый класс нелинейных волн» УФН 177 275–300 (2007); DOI: 10.3367/UFNr.0177.200703b.0275