Pulselike Exact Solutions for a Model Describing Nerve Fibers

摘要

A quasi-linear nonhomogeneous first order hyperbolic system describing nerve pulse transmission is considered. By requiring the compatibility of the governing equations with quasi-linear differential constraints, exact solutions to the model in question are determined. Furthermore classes of material response functions amenable to the mathematical approach are characterized. Initial and/or boundary value problems of interest in nerve pulse propagation are solved. It is proved that the governing model admits solutions which describe a "space clamp" situation and the propagation of a localized action potential pulse along the nerve.