Construction and application of exact solutions of the diffusive Lotka–Volterra system: A review and new results - Cherniha, Roman; Davydovych, Vasyl’ (Communications in nonlinear science & numerical simulation, 2022)
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.