Traveling Wave Solutions of a Multistable Reaction-Diffusion Equation

摘要

The equation considered here has been considered as a model for a variety of physical phenomena including population genetics and nerve conduction. Of primary interest is the eventual behavior of solutions of this equation. One expects the solution eventually to look like a traveling wave solution; that is, one which moves with constant shape and velocity. In this paper we determine all of the traveling wave solutions of the equation, showing there are situations when there exist an infinite number of traveling wave solutions.