Symmetries and exact solutions of a reaction-diffusion system arising in population dynamics
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866912983194533888 |
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| author | Broadbridge, Philip Cherniha, Roman Davydovych, Vasyl' Marquette, Ian |
| author_facet | Broadbridge, Philip Cherniha, Roman Davydovych, Vasyl' Marquette, Ian |
| contents | A system of two cubic reaction-diffusion equations for two independent gene frequencies arising in population dynamics is studied. Depending on values of coefficients, all possible Lie and $Q$-conditional (nonclassical) symmetries are identified. A wide range of new exact solutions is constructed, including those expressible in terms of a Lambert function and not obtainable by Lie symmetries. An example of a new real-world application of the system is discussed. A general algorithm for finding Q-conditional symmetries of nonlinear evolution systems of the most general form is presented in a useful form for other researchers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_13097 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Symmetries and exact solutions of a reaction-diffusion system arising in population dynamics Broadbridge, Philip Cherniha, Roman Davydovych, Vasyl' Marquette, Ian Exactly Solvable and Integrable Systems Mathematical Physics 35B06, 35K57, 35Cxx A system of two cubic reaction-diffusion equations for two independent gene frequencies arising in population dynamics is studied. Depending on values of coefficients, all possible Lie and $Q$-conditional (nonclassical) symmetries are identified. A wide range of new exact solutions is constructed, including those expressible in terms of a Lambert function and not obtainable by Lie symmetries. An example of a new real-world application of the system is discussed. A general algorithm for finding Q-conditional symmetries of nonlinear evolution systems of the most general form is presented in a useful form for other researchers. |
| title | Symmetries and exact solutions of a reaction-diffusion system arising in population dynamics |
| topic | Exactly Solvable and Integrable Systems Mathematical Physics 35B06, 35K57, 35Cxx |
| url | https://arxiv.org/abs/2412.13097 |