We propose a general method to study the solutions to nonlinear QCD evolution equations, based on a deep analogy with the physics of traveling waves. In particular, we show that the transition to the saturation regime of high energy QCD is identical to the formation of the front of a traveling wave. Within this physical picture, we provide the expressions for the saturation scale and the gluon density profile as a function of the total rapidity and the transverse momentum. The application to the Balitsky-Kovchegov equation for both fixed and running coupling constants confirms the effectiveness of this method.

9 pages, 3 figures, references added