Non-linear unbalanced Bessel beams: Stationary conical waves supported   by nonlinear losses
  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. 
Miguel A. Porras, Alberto Parola, Daniele Faccio, Audrius Dubietis,   Paolo Di Trapani