  High parton density effects with energy obey non-linear QCD evolution
equations for which exact solutions are not known. The mathematical class to
which the non-linear Balitsky-Kovchegov equation belongs is identified, proving
the existence of asymptotic in energy traveling wave solutions which are
``universal'' i.e. independent of the initial conditions and of the precise
form of the non-linearities. This has an direct impact on geometrical scaling
and the diffusive transition to saturation, which is shown to be ``normal'' for
constant QCD coupling and ``abnormal'' for running coupling.
