Submitted:
18 December 2019
Posted:
19 December 2019
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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 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 occurred in Ukraine during the Soviet times is suggested
Keywords:
reaction-diffusion system
; lie symmetry
; exact solution
; traveling front
; community of language speakers
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