Exact nonclassical symmetry solutions of Lotka-Volterra-type population systems
Publication Name
European Journal of Applied Mathematics
Abstract
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.
Open Access Status
This publication is not available as open access
Volume
34
Issue
5
First Page
998
Last Page
1016