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Q-conditional symmetries (nonclassical symmetries) for a general class oftwo-component reaction-diffusion systems with non-constant diffusivities arestudied. The work is a natural continuation of our paper (Cherniha andDavydovych, 2012) in order to extend the results on so-called no-go case. Usingthe notion of Q-conditional symmetries of the first type, an exhaustive list ofreaction-diffusion systems admitting such symmetry is derived. The resultsobtained are compared with those derived earlier. The symmetries for reducingreaction-diffusion systems to two-dimensional dynamical systems (ODE systems)and finding exact solutions are applied. As result, multiparameter families ofexact solutions in the explicit form for nonlinear reaction-diffusion systemswith an arbitrary power-law diffusivity are constructed and their propertiesfor possible applicability are established.

Nonlinear reaction-diffusion systems with a non-constant diffusivity: conditional symmetries in no-go case