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Article

Q-Conditional Symmetries and Exact Solutions of Nonlinear Reaction–Diffusion Systems

by
Oleksii Pliukhin
Department of Mathematics, Poltava National Technical Yuriy Kondratyuk University, 24, Pershotravnevyi Prospekt, 36601 Poltava, Ukraine
Symmetry 2015, 7(4), 1841-1855; https://doi.org/10.3390/sym7041841
Submission received: 28 June 2015 / Revised: 11 September 2015 / Accepted: 1 October 2015 / Published: 16 October 2015
(This article belongs to the Special Issue Lie Theory and Its Applications)
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Abstract

A wide range of reaction–diffusion systems with constant diffusivities that are invariant under Q-conditional operators is found. Using the symmetries obtained, the reductions of the corresponding systems to the systems of ODEs are conducted in order to find exact solutions. In particular, the solutions of some reaction–diffusion systems of the Lotka–Volterra type in an explicit form and satisfying Dirichlet boundary conditions are obtained. An biological interpretation is presented in order to show that two different types of interaction between biological species can be described.
Keywords: Q-conditional symmetry; reaction–diffusion systems; exact solution; Lotka–Volterra system Q-conditional symmetry; reaction–diffusion systems; exact solution; Lotka–Volterra system

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MDPI and ACS Style

Pliukhin, O. Q-Conditional Symmetries and Exact Solutions of Nonlinear Reaction–Diffusion Systems. Symmetry 2015, 7, 1841-1855. https://doi.org/10.3390/sym7041841

AMA Style

Pliukhin O. Q-Conditional Symmetries and Exact Solutions of Nonlinear Reaction–Diffusion Systems. Symmetry. 2015; 7(4):1841-1855. https://doi.org/10.3390/sym7041841

Chicago/Turabian Style

Pliukhin, Oleksii. 2015. "Q-Conditional Symmetries and Exact Solutions of Nonlinear Reaction–Diffusion Systems" Symmetry 7, no. 4: 1841-1855. https://doi.org/10.3390/sym7041841

APA Style

Pliukhin, O. (2015). Q-Conditional Symmetries and Exact Solutions of Nonlinear Reaction–Diffusion Systems. Symmetry, 7(4), 1841-1855. https://doi.org/10.3390/sym7041841

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