  We investigate the causal propagation of the pulse through dispersive media
by very precise numerical solution of the coupled Maxwell-Bloch equations
without any approximations about the strength of the input field. We study full
nonlinear behavior of the pulse propagation through solid state media like ruby
and alexandrite. We have demonstrated that the information carried by the
discontinuity, {\it i.e}, front of the pulse, moves inside the media with
velocity $c$ even though the peak of the pulse can travel either with
sub-luminal or with super-luminal velocity. We extend the argument of
Levi-Civita to prove that the discontinuity would travel with velocity $c$ even
in a nonlinear medium.
