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

V. N. Biktashev, M. A. Tsyganov

Submitted to Nature Physics 2016/04/15. Submitted to PRL 2016/04/30. Submitted to Scientific Reports 2016/05/11. Accepted 2016/07/07. Published 2016/08/05 as SRep 6:30879

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.

Journal reference: http://www.nature.com/articles/srep30879

Preprint and/or other related files:

preprint (391K)
two components, a=0.07 (2.1M)
two components, a=0.25 (1.1M)
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three components, a=0.07 (1.9M)
three components, a=0.25 (1.1M)
three components, a=0.35 (642K)

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