Renormalization group analysis for singularities in the wave beam self-focusing problem

A singular solution of the boundary value problem for the system of equatio ns describing wave beam self-focusing is investigated by constructing renor malization group symmetries. New analytic expressions are found that charac terize the spatial evolution of a beam with an arbitrary initial profile in a medium with cubic nonlinearity. The behavior of a Gaussian beam is thoro ughly analyzed up to the moment the solution singularity is formed, and a h ypothesis is proposed for describing the solution structure after the singu larity occurs.