Non-linear diffusion of cosmic rays

The propagation of cosmic rays in the interstellar medium after their release from the sources – supernova remnants – can be attended by the development of streaming instability. The instability creates MHD turbulence that changes the conditions of particle transport and leads to a non-linear diffusion of cosmic rays. We present a self-similar solution of the equation of non-linear diffusion for particles ejected from a SNR and discuss how obtained results may change the physical picture of cosmic ray propagation in the Galaxy.