The dynamics
of short radiation pulses with intensities higher than saturation threshold
is analysed. This regime may be induced by seeding and FEL amplifier
with a high power laser, and is dominated by the interplay between slippage
and the non-linear effects associated to saturation. Simple scaling
laws governs the evolution of the pulse showing the characteristics
of a solitary wave. The behaviour of this wave in a FEL cascade will
be also analysed showing the interesting feature of passing through
the stages of a cascaded FEL and to regenerate itself at the wavelength
of the higher order harmonic.