Multi-filament structures in relativistic self-focusing
  A simple model is derived to prove the multi-filament structure of relativistic self-focusing with ultra-intense lasers. Exact analytical solutions describing the transverse structure of waveguide channels with electron cavitation, for which both the relativistic and ponderomotive nonlinearities are taken into account, are presented. 
F.Cattani, A.Kim, D.Anderson and M.Lisak