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Open AccessArticle

Exact Solutions of a Mathematical Model Describing Competition and Co-Existence of Different Language Speakers

Institute of Mathematics, National Academy of Sciences of Ukraine, 3, Tereshchenkivs’ka Street, 01004 Kyiv, Ukraine
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Entropy 2020, 22(2), 154; https://doi.org/10.3390/e22020154
Received: 18 December 2019 / Revised: 16 January 2020 / Accepted: 24 January 2020 / Published: 28 January 2020
(This article belongs to the Special Issue Applications of Nonlinear Diffusion Equations)
The known three-component reaction–diffusion system modeling competition and co-existence of different language speakers is under study. A modification of this system is proposed, which is examined by the Lie symmetry method; furthermore, exact solutions in the form of traveling fronts are constructed and their properties are identified. Plots of the traveling fronts are presented and the relevant interpretation describing the language shift that has occurred in Ukraine during the Soviet times is suggested. View Full-Text
Keywords: reaction–diffusion system; Lie symmetry; exact solution; traveling front; community of language speakers; tanh method reaction–diffusion system; Lie symmetry; exact solution; traveling front; community of language speakers; tanh method
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Cherniha, R.; Davydovych, V. Exact Solutions of a Mathematical Model Describing Competition and Co-Existence of Different Language Speakers. Entropy 2020, 22, 154.

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