Conditional symmetries and exact solutions of nonlinear reaction-diffusion systems with non-constant diffusivities |
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Authors: | Roman Cherniha Vasyl’ Davydovych |
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Institution: | Institute of Mathematics, Ukrainian National Academy of Sciences, 3, Tereshchenkivs’ka Street, Kyiv 01601, Ukraine |
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Abstract: | Q-conditional symmetries (nonclassical symmetries) for the general class of two-component reaction-diffusion systems with non-constant diffusivities are studied. Using the recently introduced notion of Q-conditional symmetries of the first type, an exhausted list of reaction-diffusion systems admitting such symmetry is derived. The results obtained for the reaction-diffusion systems are compared with those for the scalar reaction-diffusion equations. The symmetries found for reducing reaction-diffusion systems to two-dimensional dynamical systems, i.e., ODE systems, and finding exact solutions are applied. As result, multiparameter families of exact solutions in the explicit form for a nonlinear reaction-diffusion system with an arbitrary diffusivity are constructed. Finally, the application of the exact solutions for solving a biologically and physically motivated system is presented. |
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Keywords: | Nonlinear reaction-diffusion system Lie symmetry Q-conditional symmetry Non-classical symmetry Exact solution |
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