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q-conditional symmetry

European Journal of Applied Mathematics (1)

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1 results

Conditional symmetries and exact solutions of a nonlinear three-component reaction-diffusion model
Part of
- Parabolic equations and systems
- Partial differential equations
R. M. CHERNIHA, V. V. DAVYDOVYCH
Journal:

European Journal of Applied Mathematics / Volume 32 / Issue 2 / April 2021

Published online by Cambridge University Press:

11 May 2020, pp. 280-300
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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.