Exact Nonclassical Symmetry Solutions of Lotka-Volterra Type Population Systems
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929264684695552 |
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| author | Broadbridge, Phillip Cherniha, Roman Goard, Joanna |
| author_facet | Broadbridge, Phillip Cherniha, Roman Goard, Joanna |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_02644 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Exact Nonclassical Symmetry Solutions of Lotka-Volterra Type Population Systems Broadbridge, Phillip Cherniha, Roman Goard, Joanna Exactly Solvable and Integrable Systems Analysis of PDEs 35K40 (Primary), 92D25, 35K57, 35C05, 35B06 (Secondary) 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. |
| title | Exact Nonclassical Symmetry Solutions of Lotka-Volterra Type Population Systems |
| topic | Exactly Solvable and Integrable Systems Analysis of PDEs 35K40 (Primary), 92D25, 35K57, 35C05, 35B06 (Secondary) |
| url | https://arxiv.org/abs/2403.02644 |