  Nonlinear losses accompanying Kerr self-focusing substantially impacts the
dynamic balance of diffraction and nonlinearity, permitting the existence of
localized and stationary solutions of the 2D+1 nonlinear Schrodinger equation
which are stable against radial collapse. These are featured by linear conical
tails that continually refill the nonlinear, central spot. An experiment shows
that the discovered solution behaves as strong attractor for the self-focusing
dynamics in Kerr media.
