Quasisolitons in self-diffusive excitable systems, or Why asymmetric diffusivity obeys the Second Law

Abstract

Quasi-solitons are waves in excitable systems that reflect from boundaries and pass through each other, similarly to solitons in conservative systems. Previously, they have been observed at finely tuned parameters or in systems with cross-diffusion. Here we demonstrate quasi-solitons robustly occuring in excitable systems with self-diffusion only. This is due to effective cross-diffusion emerging via adiabatic elimination of fast but diffusing components. The elimination procedure can be used to find interesting wave regimes in complex, stiff systems by studying simpler, soft systems.