Conditional symmetries and exact solutions of a nonlinear three-component reaction-diffusion model
Mathematical Physics
2021-01-01 v1 math.MP
Abstract
Q-conditional (nonclassical) symmetries of the known three-component reaction-diffusion system [K. Aoki et al Theor. Pop. Biol. 50(1) (1996)] modeling interaction between farmers and hunter-gatherers are constructed for the first time. A wide variety of Q-conditional symmetries are found in an explicit form and it is shown that these symmetries are not equivalent to the Lie symmetries. Some operators of Q-conditional (nonclassical) symmetry are applied for finding exact solutions of the reaction-diffusion system in question. Properties of the exact solutions (in particular, their asymptotic behaviour) are identified and possible biological interpretation is discussed.
Cite
@article{arxiv.1911.12973,
title = {Conditional symmetries and exact solutions of a nonlinear three-component reaction-diffusion model},
author = {Roman Cherniha and Vasyl' Davydovych},
journal= {arXiv preprint arXiv:1911.12973},
year = {2021}
}