Controlled complexity in pulse conduction: Traveling solitons from neural to optical fibers

Abstract

We review and analyze models of controlled complexity in nonlinear pulse conduction, ranging from the Hodgkin-Huxley action potentials propagating along neural fibers to rogue waves
in optical fibers. The novel model proposed is an alternative to the Hodgkin-Huxley neural model in the form of the sine-Gordon wave equation. This new alternative explains pulse conduction in terms of general wave phenomena (such as kinks, solitons and breathers).