New conditional symmetries and exact solutions of reaction-diffusion   systems with power diffusivities
  A wide range of new Q-conditional symmetries for reaction-diffusion systems with power diffusivities are constructed. The relevant non-Lie ansatze to reduce the reaction-diffusion systems to ODE systems and examples of exact solutions are obtained. The relation of the solutions obtained with the development of spatially inhomogeneous structures is discussed. 
Roman Cherniha, Oleksii Pliukhin