The renormalization-group approach to solving the equation of nonlinear transfer

With the help of an example of the equation of nonlinear transfer with power nonlinearity, it is shown how the requirement of functional self-similarity (renormalization invariance) enables one to construct a solution to the equation. Using this approach, the functional forms of the solution and additional conditions allowed are found by solving linear differential equations of the renormalization group, and the original nonlinear equation is only used for finding the numerical parameters of the solution (power exponents and coefficients). In addition, we present exact solutions to a transfer equation of a more general type that includes coordinates and space derivatives to arbitrary power.