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Exact Nonclassical Symmetry Solutions of Lotka-Volterra Type Population Systems
Published 5 Mar 2024 in nlin.SI and math.AP | (2403.02644v1)
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, related to the diffusive Lotka-Volterra system, are constructed. An infinite dimensional class of exact solutions is made available. Unlike in the standard Lotka-Volterra system, in the absence of predators, the prey population has a finite carrying capacity, as in the Fisher equation.
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