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Conditional symmetries and exact solutions of a nonlinear three-component reaction-diffusion model

Part of: Partial differential equations Parabolic equations and systems

Published online by Cambridge University Press:  11 May 2020

R. M. CHERNIHA Open the ORCID record for R. M. CHERNIHA [Opens in a new window]  and
V. V. DAVYDOVYCH
R. M. CHERNIHA
Affiliation:
Institute of Mathematics, NAS of Ukraine, 3 Tereshchenkivs’ka Street, 01004 Kyiv, Ukraine, emails: r.m.cherniha@gmail.com; davydovych@imath.kiev.ua
V. V. DAVYDOVYCH
Affiliation:
Institute of Mathematics, NAS of Ukraine, 3 Tereshchenkivs’ka Street, 01004 Kyiv, Ukraine, emails: r.m.cherniha@gmail.com; davydovych@imath.kiev.ua
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Abstract

Q-conditional (non-classical) symmetries of the known three-component reaction-diffusion (RD) system [K. Aoki et al. Theor. Popul. Biol. 50, 1–17 (1996)] modelling interaction between farmers and hunter-gatherers are constructed for the first time. A wide variety of Q-conditional symmetries are found, and it is shown that these symmetries are not equivalent to the Lie symmetries. Some operators of Q-conditional (non-classical) symmetry are applied for finding exact solutions of the RD system in question. Properties of the exact solutions (in particular, their asymptotic behaviour) are identified and possible biological interpretation is discussed.

Keywords

Reaction-diffusion systemhunter-gatherer–farmer systemLie symmetryQ-conditional symmetryexact solution

MSC classification

Primary: 35B06: Symmetries, invariants, etc.
Secondary: 35K57: Reaction-diffusion equations
Type
Papers
Information
European Journal of Applied Mathematics , Volume 32 , Issue 2 , April 2021 , pp. 280 - 300
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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