Construction and application of exact solutions of the diffusive Lotka–Volterra system: A review and new results

This review summarizes all known results (up to this date) about methods of integration of the classical Lotka–Volterra systems with diffusion and presents a wide range of exact solutions, which are the most important from applicability point of view. It is the first attempt in this direction. Becau...

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Bibliographic Details
Published in:Communications in nonlinear science & numerical simulation Vol. 113; p. 106579
Main Authors: Cherniha, Roman, Davydovych, Vasyl’
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 01.10.2022
Elsevier Science Ltd
Subjects:
Applications of mathematics
Approximation
Boundary value problems
Diffusive Lotka–Volterra system
Exact solution
Exact solutions
Lie and conditional symmetry
Mathematical models
Numerical analysis
Numerical methods
Population dynamics
Traveling front
Lie and conditional symmetry
Traveling front
Population dynamics
Diffusive Lotka–Volterra system
Exact solution
ISSN:1007-5704, 1878-7274
Online Access:Get full text
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Summary:This review summarizes all known results (up to this date) about methods of integration of the classical Lotka–Volterra systems with diffusion and presents a wide range of exact solutions, which are the most important from applicability point of view. It is the first attempt in this direction. Because the diffusive Lotka–Volterra systems are used for mathematical modeling enormous variety of processes in ecology, biology, medicine, physics and chemistry, the review should be interesting not only for specialists from Applied Mathematics but also those from other branches of Science. The obtained exact solutions can also be used as test problems for estimating the accuracy of approximate analytical and numerical methods for solving relevant boundary value problems. •All known results about integration methods of the diffusive Lotka–Volterra systems are summarized.•Wide sets of exact solutions, including traveling fronts, are presented.•Plots and biological interpretation of the most interesting solutions are presented.•Some unsolved problems are highlighted.
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ISSN:1007-5704
1878-7274
DOI:10.1016/j.cnsns.2022.106579