Generation, interaction and reduction of filaments as a nonlinear   process
  The absence of ionization and observation of white continuum in the initial moment of filamentation of powerful femtosecond laser pulses, propagating in silica glasses, as well as the filamentation without plasma channels observed in the experiments in air, forced us to look for other nonlinear mechanisms of description the above mentioned effects. For this reason we present in this paper new parametric conversion mechanism for asymmetric spectrum broadening of femtosecond laser pulses towards the higher frequencies in isotropic media. This mechanism includes cascade generation with THz spectral shift for solids and GHz spectral delay for gases. The process works simultaneously with the four-photon parametric wave mixing. The proposed theoretical model gives very good coincidence with the experimental data. In addition we demonstrate that the nonlinear model describes the process of reduction of the number of filaments trough two mechanisms of nonlinear interaction: attraction due to cross-phase modulation and energy exchange due to four-photon parametric wave mixing. 
L. M. Kovachev, D.A. Georgieva and N. Nedyalkov
physics.optics nlin.PS