Solitary waves in excitable systems with cross-diffusion

V. N. Biktashev, M. A. Tsyganov

Submitted to Proc Roy Soc London A: June 2, 2004. Referee comments received: January 10, 2005. Submitted in resived form: February 18, 2005. Accepted for publication: June 6, 2005. Submitted in final form: June 15, 2005

We consider a FitzHugh-Nagumo system of equations where the traditional diffusion terms are replaced with linear cross-diffusion of components. This system describes solitary waves that have unusual form and are capable of quasi-soliton interaction. This is different from the classical FitzHugh-Nagumo system with self-diffusion, but similar to a predator-prey model with taxis of populations on each other's gradient which we considered earlier. We study these waves by numerical simulations and also present an analytical theory, based on the asymptotic behaviour which arises when the local dynamics of the inhibitor field are much slower than those of the activator field.