Reviews of topical problems

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

 a,  b,  c,  d,  a
a Institute for Theoretical and Experimental Biophysics, Russian Academy of Sciences, Institutskaya str. 3, Pushchino, Moscow Region, 142290, Russian Federation
b Department of Mathematical Sciences, University of Liverpool, Liverpool, UK
c Department of Applied Mathematics, University of Leeds, Leeds, UK
d Faculty 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.

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Fulltext is also available at DOI: 10.1070/PU2007v050n03ABEH006114
PACS: 05.45.−a, 87.18.Hf, 87.23.Cc (all)
DOI: 10.1070/PU2007v050n03ABEH006114
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

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