Existence, Uniqueness and Classification of Plane Waves

TL;DR

This paper establishes the existence, uniqueness, and classification of plane wave solutions supported by irreversible reactions, using a novel proof technique that extends to cutoff reactions, providing a rigorous mathematical framework.

Contribution

It introduces a new proof method for guaranteeing unique plane waves at each wavespeed above a threshold, extending classical results to cutoff reactions.

Findings

Unique plane waves exist for all wavespeeds above a threshold.

The method extends to reactions with cutoff thresholds.

The proof technique offers a new approach to classical results.

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.