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Analytical properties and exact solutions of the Lotka–Volterra competition system

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  • Kudryashov, Nikolay A.
  • Zakharchenko, Anastasia S.

Abstract

The Lotka–Volterra competition system with diffusion is considered. The Painlevé property of this system is investigated. Exact traveling wave solutions of the Lotka–Volterra competition system are found. Periodic solutions expressed in terms of the Weierstrass elliptic function are also given.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:254:y:2015:i:c:p:219-228
    DOI: 10.1016/j.amc.2014.12.113
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    References listed on IDEAS

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    1. Kudryashov, Nikolai A., 2005. "Simplest equation method to look for exact solutions of nonlinear differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 24(5), pages 1217-1231.
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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.
    2. 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.

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