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

M A Tsyganov, V N Biktashev, J Brindley, A V Holden, G R Ivanitsky

Submitted 2006/04/28. Revised 2006/07/18. Published UFN 177(3):233-234 (Physics-Uspekhi 50(3):275-300), March 2007

Research on spatially-extended excitable systems with cross-diffusing 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 non-soliton 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 taxis. 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.