Exact Propagating Wave Solutions in Reaction Cross-Diffusion System

2020/04/16 by Aldurayhim, Abdullah, Biktashev, Vadim N.
#FOS: Physical sciences #Pattern Formation and Solitons (nlin.PS)

paper · doi:10.48550/arxiv.2004.07962

Abstract

Reaction-diffusion systems with cross-diffusion terms in addition to, or instead of, the usual self-diffusion demonstrate interesting features which motivate their further study. The present work is aimed at designing a toy reaction-cross-diffusion model with exact solutions in the form of propagating fronts. We propose a minimal model of this kind which involves two species linked by cross-diffusion, one of which governed by a linear equation and the other having a polynomial kinetic term. We classify the resulting exact propagating front solutions. Some of them have some features of the Fisher-KPP fronts and some features of the ZFK-Nagumo fronts.

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