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