Multi-species reaction-diffusion models admitting shock solutions

TL;DR

This paper introduces a classification method for multi-species reaction-diffusion models that admit shock solutions, focusing on two-species models with specific stationary states and exploring their phase transitions.

Contribution

It presents a novel classification framework for reaction-diffusion models with shock solutions, extending from two-species to multi-species systems, and analyzes their phase transition behavior.

Findings

Two-species models admit single-shock solutions under certain constraints.

Generalization to multi-species models broadens applicability.

Dynamical phase transitions are characterized in these models.

Abstract

A method for classifying $n$-species reaction-diffusion models, admitting shock solutions is presented. The most general one-dimensional two-species reaction-diffusion model with nearest neighbor interactions admitting uniform product measures as the stationary states is studied. Satisfying more constraints, these models may experience single-shock solutions. These models are generalized to multi-species models. The two-species models are studied in detail. Dynamical phase transitions of such models are also investigated.