CLASS OF EXACTLY SOLVABLE MODELS OF EXCITABLE MEDIA

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 contro l variable. A pulse solution can be found in the entire domain without any use of singular perturbation theory. We reduce the nonlinear eige nvalue problem for a steadily propagating one-dimensional pulse to a s et of transcendental equations which can be compactly solved analytica lly within any power of the smallness parameter epsilon.