Quasisolitons in self-diffusive excitable systems, or Why asymmetric diffusivity does not violate the Second Law

TL;DR

This paper demonstrates that quasi-solitons, resembling classical solitons, can be robustly observed in self-diffusive excitable systems, explained by effective cross-diffusion emerging from adiabatic elimination.

Contribution

It shows that quasi-solitons can exist in excitable systems with only self-diffusion, expanding understanding of wave phenomena in dissipative systems.

Findings

Quasi-solitons observed with self-diffusion only.

Effective cross-diffusion explains quasi-soliton formation.

Reduction procedure aids in studying complex wave regimes.

Abstract

Solitons, defined as nonlinear waves which can reflect from boundaries or transmit through each other, are found in conservative, fully integrable systems. Similar phenomena, dubbed quasi-solitons, have been observed also in dissipative, "excitable" systems, either at finely tuned parameters (near a bifurcation) or in systems with cross-diffusion. Here we demonstrate that quasi-solitons can be robustly observed in excitable systems with excitable kinetics and with self-diffusion only. This includes quasi-solitons of fixed shape (like KdV solitons) or envelope quasi-solitons (like NLS solitons). This can happen in systems with more than two components, and can be explained by effective cross-diffusion, which emerges via adiabatic elimination of a fast but diffusing component. We describe here a reduction procedure can be used for the search of complicated wave regimes in multi-component, stiff systems by studying simplified, soft systems.