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Exact Solutions of a Mathematical Model Describing Competition and Co-Existence of Different Language Speakers
Roman Cherniha1, Vasyl' Davydovych1
1Institute of Mathematics, National Academy of Sciences of Ukraine, 3, Tereshchenkivs'ka Street, 01004 Kyiv, Ukraine.
Abstract:
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.
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