  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.
