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

Source: [Quasisolitons in self-diffusive excitable systems, or Why asymmetric diffusivity does not violate the Second Law](<https://www.sota2.com/research/paper/68fa33db1e209131ce893bee>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T20:18:59.854Z

Authors: V. N. Biktashev, M. A. Tsyganov

Published: 2016-05-02T15:18:59.000Z

## 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.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1605.00521>)

[PDF](<https://arxiv.org/pdf/1605.00521.pdf>)