Pulselike exact solutions for a model describing nerve fibers

A quasi-linear nonhomogeneous first order hyperbolic system describing nerv e pulse transmission is considered. By requiring the compatibility of the g overning equations with quasi-linear differential constraints, exact soluti ons to the model in question are determined. Furthermore classes of materia l response functions amenable to the mathematical approach are characterize d. Initial and/or boundary value problems of interest in nerve pulse propag ation are solved. It is proved that the governing model admits solutions wh ich describe a "space clamp" situation and the propagation of a localized a ction potential pulse along the nerve.