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UFN, 2007, Volume 177, Number 3, Pages 275–300 (Mi ufn438)  

This article is cited in 37 scientific papers (total in 37 papers)

REVIEWS OF TOPICAL PROBLEMS

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.

DOI: https://doi.org/10.3367/UFNr.0177.200703b.0275

Full text: PDF file (6512 kB)
Full text: http://www.ufn.ru/ru/articles/2007/3/b/
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English version:
Physics–Uspekhi, 2007, 50:3, 263–286

Bibliographic databases:

PACS: 05.45.-a, 87.18.Hf, 87.23.Cc
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

Citation in format AMSBIB
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\yr 2007
\vol 177
\issue 3
\pages 275--300
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\crossref{https://doi.org/10.3367/UFNr.0177.200703b.0275}
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