Analytical properties and exact solutions of the Lotka--Volterra competition system
Nikolay A. Kudryashov, Anastasia S. Zakharchenko
TL;DR
This paper investigates the mathematical properties of the diffusive Lotka--Volterra competition system, establishing its Painlevé property and deriving exact solutions including traveling waves and periodic elliptic functions.
Contribution
It provides new analytical insights and explicit solutions for the Lotka--Volterra competition system with diffusion, including its Painlevé property and elliptic function solutions.
Findings
The system possesses the Painlevé property.
Exact traveling wave solutions are derived.
Periodic solutions are expressed via Weierstrass elliptic functions.
Abstract
The Lotka--Volterra competition system with diffusion is considered. The Painlev\'e property of this system is investigated. Exact traveling wave solutions of the Lotka--Volterra competition system are found. Periodic solutions expressed in terms of the Weierstrass elliptic function are also given.
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Taxonomy
TopicsMathematical and Theoretical Epidemiology and Ecology Models · Advanced Differential Equations and Dynamical Systems · Nonlinear Waves and Solitons