Traveling kinks in discrete media: Exact solution in a piecewise linear model

We present an exact integral representation of a traveling kink solution in a reaction-diffusion equation with a piecewise linear reaction function, complementing existence proofs and numerical observations of such solutions in discrete excitable media. The kink speed is determined through a matching condition, and is worked out explicitly in two limiting situations: the pinning limit, and the opposite limit of infinitely fast kink. Results on the pinning limit agree with those in a recent paper by Fath [Physica D 116, 176 (1998)]. The model includes a "recovery parameter" for a possible extension to a discrete FitzHugh-Nagumo-type system.