Nonlinear beam tapering and two-dimensional ring solitons

We examine a possibility to exploit the nonlinear lens effect - the initial stage of self-focusing to localize initially broad field distribution into the small central area where wave collapse is arrested - the nonlinear beam tapering. We describe two-dimensional localized solitary waves (ring solitons) in a physical system that presents a linear medium in the central core, surrounded by the cladding with the focusing Kerr nonlinearity. The standard variational analysis demonstrates that such solitons correspond to the minimum of the Hamiltonian.