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arXiv · 2403.02644

Exact Nonclassical Symmetry Solutions of Lotka-Volterra Type Population Systems

Phillip Broadbridge·Roman Cherniha·Joanna Goard
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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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Phillip Broadbridge, Roman Cherniha, Joanna Goard. 2024-03-05. Exact Nonclassical Symmetry Solutions of Lotka-Volterra Type Population Systems. https://doi.org/10.1017/s095679252200033x

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