Complete Classification of Traveling Waves and Resolution of Linear Conjecture in Monostable Systems

TL;DR

This paper provides a comprehensive classification of traveling wave solutions in monostable systems using a new slicing method based on super- and sub-solutions, resolving a longstanding linear conjecture.

Contribution

It introduces the slicing method, a novel technique for classifying traveling waves in monostable systems, unifying previous fragmented approaches.

Findings

Complete classification of traveling wave solutions

Resolution of the linear conjecture in monostable systems

Introduction of the slicing method for analysis

Abstract

In this paper, we present a complete classification of traveling wave solutions for monostable systems within a unified framework. To this end, we introduce a novel technique, referred to as the slicing method, which is based on the construction of suitable super- and sub-solutions.