Exact Nonclassical Symmetry Solutions of Lotka-Volterra Type Population Systems
arXiv:2403.02644 · doi:10.1017/S095679252200033X
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.
arXiv comment8 figures
References in corpus (8)
- Conditional symmetries and exact solutions of the diffusive Lotka-Volterra system
- Exact solutions for logistic reaction-diffusion in biology
- Construction and application of exact solutions of the diffusive Lotka-Volterra system: a review and new results
- Lie and conditional symmetries of the three-component diffusive Lotka - Volterra system
- Exact nonclassical symmetry solutions of Arrhenius reaction-diffusion
- A hunter-gatherer-farmer population model: Lie symmetries, exact solutions and their interpretation
- Conditional symmetries and exact solutions of a nonlinear three-component reaction-diffusion model
- Exact solutions of a mathematical model describing competition and co-existence of different language speakers