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arXiv · 1605.00521

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

V. N. Biktashev·M. A. Tsyganov
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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.

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V. N. Biktashev, M. A. Tsyganov. 2016-07-07. Quasisolitons in self-diffusive excitable systems, or Why asymmetric diffusivity does not violate the Second Law. https://doi.org/10.1038/srep30879

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