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New Conditional Symmetries and Exact Solutions of the Diffusive Two-Component Lotka–Volterra System

Author

Listed:
  • Roman Cherniha

    (Institute of Mathematics, National Academy of Sciences of Ukraine, 3, Tereshchenkivs’ka Street, 01601 Kyiv, Ukraine)

  • Vasyl’ Davydovych

    (Institute of Mathematics, National Academy of Sciences of Ukraine, 3, Tereshchenkivs’ka Street, 01601 Kyiv, Ukraine)

Abstract

The diffusive Lotka–Volterra system arising in an enormous number of mathematical models in biology, physics, ecology, chemistry and society is under study. New Q -conditional (nonclassical) symmetries are derived and applied to search for exact solutions in an explicit form. A family of exact solutions is examined in detail in order to provide an application for describing the competition of two species in population dynamics. The results obtained are compared with those published earlier as well.

Suggested Citation

  • Roman Cherniha & Vasyl’ Davydovych, 2021. "New Conditional Symmetries and Exact Solutions of the Diffusive Two-Component Lotka–Volterra System," Mathematics, MDPI, vol. 9(16), pages 1-17, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:16:p:1984-:d:617463
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    References listed on IDEAS

    as
    1. Kudryashov, Nikolay A. & Zakharchenko, Anastasia S., 2015. "Analytical properties and exact solutions of the Lotka–Volterra competition system," Applied Mathematics and Computation, Elsevier, vol. 254(C), pages 219-228.
    2. Cherniha, Roman & Davydovych, Vasyl’, 2015. "Nonlinear reaction–diffusion systems with a non-constant diffusivity: Conditional symmetries in no-go case," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 23-34.
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    Cited by:

    1. Andrei D. Polyanin & Alexei I. Zhurov, 2022. "Multi-Parameter Reaction–Diffusion Systems with Quadratic Nonlinearity and Delays: New Exact Solutions in Elementary Functions," Mathematics, MDPI, vol. 10(9), pages 1-28, May.

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    1. Andrei D. Polyanin & Alexei I. Zhurov, 2022. "Multi-Parameter Reaction–Diffusion Systems with Quadratic Nonlinearity and Delays: New Exact Solutions in Elementary Functions," Mathematics, MDPI, vol. 10(9), pages 1-28, May.

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