title: Segregation and pursuit waves in activator-inhibitor systems.
abstract: We investigate the effects of cross-diffusion on propagating waves in an activator-inhibitor system. The model consists of a piecewise linear approximation of FitzHugh-Nagumo kinetics and a cross-diffusion term for either the activator or the inhibitor. We obtain exact analytic solutions for traveling fronts and solitary pulses and discuss the corresponding speed diagrams. A detailed comparison with the corresponding Rinzel-Keller model for the usually studied case of self-diffusion is performed.
authors.affiliation: Grup de Física Estadística, Departament de Física, Facultat de Ciències, Edicifi Cc. Universitat Autònoma de Barcelona, E-08193 Bellaterra (Barcelona), Spain.
authors.forename: Vicenç
authors.initials: V
authors.lastname: Méndez
authors.forename: Werner
authors.initials: W
authors.lastname: Horsthemke
authors.forename: Evgeny P
authors.initials: EP
authors.lastname: Zemskov
authors.forename: José
authors.initials: J
authors.lastname: Casas-Vázquez