English

Exact Nonclassical Symmetry Solutions of Lotka-Volterra Type Population Systems

Exactly Solvable and Integrable Systems 2024-03-06 v1 Analysis of PDEs

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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Cite

@article{arxiv.2403.02644,
  title  = {Exact Nonclassical Symmetry Solutions of Lotka-Volterra Type Population Systems},
  author = {Phillip Broadbridge and Roman Cherniha and Joanna Goard},
  journal= {arXiv preprint arXiv:2403.02644},
  year   = {2024}
}

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