Exact nonclassical symmetry solutions of Lotka–Volterra-type population systems
Published online by Cambridge University Press: 25 November 2022
New classes of conditionally integrable systems of nonlinear reaction–diffusion equations are introduced. They are obtained by extending a well-known nonclassical symmetry of a scalar partial differential equation to a vector equation. New exact solutions of nonlinear predator–prey systems with cross-diffusion are constructed. Infinite dimensional classes of exact solutions are made available for such nonlinear systems. Some of these solutions decay towards extinction and some oscillate or spiral around an interior fixed point. It is shown that the conditionally integrable systems are closely related to the standard diffusive Lotka–Volterra system, but they have additional features.
- European Journal of Applied Mathematics , Volume 34 , Special Issue 5: Symmetries and Differential Equations , October 2023 , pp. 998 - 1016
- © The Author(s), 2022. Published by Cambridge University Press