title: Quasisolitons in self-diffusive excitable systems, or Why asymmetric diffusivity obeys the Second Law.
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.
authors.affiliation: College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter EX4 4QF, UK.|EPSRC Centre for Predictive Modelling in Healthcare, University of Exeter, Exeter, EX4 4QJ, UK.
authors.forename: V N
authors.initials: VN
authors.lastname: Biktashev
authors.affiliation: Institute of Theoretical and Experimental Biophysics, Pushchino, Moscow Region, 142290, Russia.
authors.forename: M A
authors.initials: MA
authors.lastname: Tsyganov