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This article is cited in 59 scientific papers (total in 59 papers)
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Waves in systems with cross-diffusion as a new class of nonlinear waves
M. A. Tsyganova, V. N. Biktashevb, J. Brindleyc, A. V. Holdend, G. R. Ivanitskiia a Institute for Theoretical and Experimental Biophysics, Russian Academy of Sciences
b Department of Mathematical Sciences, University of Liverpool
c Department of Applied Mathematics, University of Leeds
d Faculty of Biological Sciences, University of Leeds
Abstract:
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.
Received: April 28, 2006 Revised: July 18, 2006
Citation:
M. A. Tsyganov, V. N. Biktashev, J. Brindley, A. V. Holden, G. R. Ivanitskii, “Waves in systems with cross-diffusion as a new class of nonlinear waves”, UFN, 177:3 (2007), 275–300; Phys. Usp., 50:3 (2007), 263–286
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https://www.mathnet.ru/eng/ufn438 https://www.mathnet.ru/eng/ufn/v177/i3/p275
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