Drifting solitary waves in a reaction-diffusion medium with differential advection

TL;DR

This paper investigates drifting solitary waves in reaction-diffusion systems with differential advection, revealing how convective instability leads to propagating pulses and offering insights into localized transport in chemical and biological contexts.

Contribution

It provides a spatial dynamics analysis of drifting solitary waves caused by differential advection in reaction-diffusion systems, enhancing understanding of their formation and organization.

Findings

Drifting pulses form via convective instability at low reaction rates.

Advection overcomes excitation, inducing fluid-like propagating behavior.

The study offers a framework for understanding localized transport in reaction-diffusion-advection models.

Abstract

Propagation of solitary waves in the presence of autocatalysis, diffusion, and symmetry breaking (differential) advection, is being studied. The focus is on drifting (propagating with advection) pulses that form via a convective instability at lower reaction rates of the autocatalytic activator, i.e. the advective flow overcomes the fast excitation and induces a drifting fluid type behavior. Using spatial dynamics analysis of a minimal case model, we present the properties and the organization of such pulses. The insights underly a general understanding of localized transport in simple reaction-diffusion-advection models and thus provide a background to potential chemical and biological applications.