  Optical propagation and vortices in nonlinear media have been intensively
studied in modern optical physics. In this paper, we establish constraints
regarding the propagation constant and provide an existence theory and
numerical computations for positive exponentially decaying solutions for a
class of ring-profiled solitons in a type of nonlinear media known as a
photorefractive nonlinearity. Our methods include constrained minimization and
finite element formalism, and we study the vortex profile and its propagation
by fixing the energy flux.
