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Q-conditional symmetries (nonclassical symmetries) for the general class oftwo-component reaction-diffusion systems with non-constant diffusivities arestudied. Using the recently introduced notion of Q-conditional symmetries ofthe first type, an exhausted list of reaction-diffusion systems admitting suchsymmetry is derived. The results obtained for the reaction-diffusion systemsare compared with those for the scalar reaction-diffusion equations. Thesymmetries found for reducing reaction-diffusion systems to two-dimensionaldynamical systems, i.e., ODE systems, and finding exact solutions are applied.As result, multiparameter families of exact solutions in the explicit form fora nonlinear reaction-diffusion system with an arbitrary diffusivity areconstructed. Finally, the application of the exact solutions for solving abiologically and physically motivated system is presented.

Conditional symmetries and exact solutions of nonlinear reaction-diffusion systems with non-constant diffusivities