I will discuss saturation as described by the Balitsky-Kovchegov (BK) equation. The BK equation has been solved analytically by Munier and Peschanski in the transition region to saturation, in terms of traveling wave fronts. I give a brief overview of their method and go on to study the numerical solution of the BK equation. The traveling wave results agree very well with the full solutions.
I will also discuss the fluctuation of dipole sizes in a QCD dipole cascade, by studying the extreme value statistics of maximum and minimum sizes. We have derived the equation describing the distributions of maximum and minimum sizes. It is equivalent to the BK equation, and the distributions thus have traveling wave solutions and obey a new type of geometrical scaling. This gives a new perspective on the study of dipole fluctuations.

SPhT, CEA/Saclay