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.
Lahiri
Avijit
A
Department of Physics, Vidyasagar Evening College, Kolkata 700 006, India.
Majumdar
Priyadarshi
P
Roy
Mahendra Sinha
MS