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

Entropy (Basel). 2020 Jan 28;22(2):154. doi: 10.3390/e22020154.


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.

Keywords: Lie symmetry; community of language speakers; exact solution; reaction–diffusion system; tanh method; traveling front.