Existence, Uniqueness and Classification of Plane Waves

Abstract

Existence, uniqueness and classification is established for plane waves supported by an irreversible reaction which is a smooth function of local reactant and product concentrations (or prey and predator populations). Rudimentary analytic techniques are used to guarantee a unique plane wave at every wavespeed $V>V_*$ above some threshold. The result readily extends to cutoff reactions, which are zero below some threshold product concentration. These results are not novel, but the method of proof is.