Similarity solution of two coupled reaction-diffusion rate equations

A coupled system of nonlinear evolution equations describing the combined effects of diffusion and reactions, e.g., fusion reactions or electron-ion recombinations, is transformed into a system of coupled similarity equations in one, two, and three dimensions. A description of the evolution of the coupled system for special though physically relevant situations, e.g., the diffusion of an ignited high-density fusion plasma (thermal-thermal reactions) of tritium and deuterium, is obtained in terms of a particular similarity solution.