Nonlinear reaction-diffusion systems with a non-constant diffusivity: Conditional symmetries in no-go case
Q-conditional symmetries (nonclassical symmetries) for a general class of two-component reaction-diffusion systems with non-constant diffusivities are studied. The work is a natural continuation of our paper "Conditional symmetries and exact solutions of nonlinear reaction-diffusion systems with non-constant diffusivities" (Cherniha and Davydovych, 2012) 1 in order to extend the results on so-called no-go case. Using the notion of Q-conditional symmetries of the first type, an exhaustive list of reaction-diffusion systems admitting such symmetry is derived. The results obtained are compared with those derived earlier. The symmetries for reducing reaction-diffusion systems to two-dimensional dynamical systems (ODE systems) and finding exact solutions are applied. As result, multiparameter families of exact solutions in the explicit form for nonlinear reaction-diffusion systems with an arbitrary power-law diffusivity are constructed and their properties for possible applicability are established.