RENORMALIZATION-GROUP SYMMETRIES IN PROBLEMS OF NONLINEAR GEOMETRICAL-OPTICS

We construct renormalization group symmetries in the geometrical optic s approximation for the boundary value problem of the system of equati ons describing the propagation of strong radiation in a nonlinear medi um. Using the renormalization group symmetries, new exact and approxim ate analytic solutions to the equations of nonlinear geometrical optic s are obtained. Explicit analytic expressions are presented that chara cterize the spatial evolution of a laser beam having an arbitrary depe ndence on intensity at the nonlinear medium boundary.