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

被引：7

作者：

Cherniha, R. M. ^{[1
]}

Davydovych, V. V. ^{[1
]}

机构：

[1] NAS Ukraine, Inst Math, 3 Tereshchenkivska St, UA-01004 Kviv, Ukraine

来源：

EUROPEAN JOURNAL OF APPLIED MATHEMATICS | 2021年 / 32卷 / 02期

关键词：

Reaction-diffusion system; hunter-gatherer-farmer system; Lie symmetry; Q-conditional symmetry; exact solution; LIE-BACKLUND SYMMETRY; NONCLASSICAL SYMMETRIES; REDUCTIONS; EQUATIONS; INVARIANT; SYSTEMS; EXAMPLE;

D O I：

10.1017/S0956792520000121

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：280 / 300

页数：21

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