Class of Exactly Solvable Models of Excitable Media

Abstract

We introduce a class of exactly solvable reaction diffusion models of excitable media with nondiffusive control kinetics and the source term in the diffusion equation depending only parametrically on the control variable. A pulse solution can be found in the entire domain without any use of singular perturbation theory. We reduce the nonlinear eigenvalue problem for a steadily propagating one-dimensional pulse to a set of transcendental equations which can be compactly solved analytically within any power of the smallness parameter $\ensuremath{\varepsilon}$.