Exact self-similar solution of a certain equation of non-linear diffusion with dissipation

Using the renormalization-group method, an exact solution of the equation of non-linear diffusion with dissipation of the Cahn–Hilliard type is obtained. When finding an admissible form of the self-similar solution, only dimensionality arguments and the property of renormalization invariance are used. The form of the initial and boundary conditions, consistent with the non-linear equation cannot be given in advance, but is found from the solution of the renormalization-group equations.