Nonlinear unbalanced Bessel beams in the collapse of Gaussian beams   arrested by nonlinear losses
  Collapse of a Gaussian beam in self-focusing Kerr media arrested by nonlinear losses may lead to the spontaneous formation of a quasi-stationary nonlinear unbalanced Bessel beam with finite energy, which can propagate without significant distortion over tens of diffraction lengths, and without peak intensity attenuation while the beam power is drastically diminishing. 
Miguel A. Porras, Alberto Parola