Conical emission, pulse splitting and X-wave parametric amplification in   nonlinear dynamics of ultrashort light pulses
  The precise observation of the angle-frequency spectrum of light filaments in water reveals a scenario incompatible with current models of conical emission (CE). Its description in terms of linear X-wave modes leads us to understand filamentation dynamics requiring a phase- and group-matched, Kerr-driven four-wave-mixing process that involves two highly localized pumps and two X-waves. CE and temporal splitting arise naturally as two manifestations of this process. 
Daniele Faccio, Miguel A. Porras, Audrius Dubietis, Francesca   Bragheri, Arnaud Couairon, Paolo Di Trapani