We show that the HERA data for the inclusive structure function F 2 (x, Q 2 ) for x ≤ 10 −2 and 0.045 ≤ Q 2 ≤ 45 GeV 2 can be well described within the color dipole picture, with a simple analytic expression for the dipole-proton scattering amplitude, which is an approximate solution to the non-linear evolution equations in QCD. For dipole sizes less than the inverse saturation momentum 1/Q s (x), the scattering amplitude is the solution to the BFKL equation in the vicinity of the saturation line. It exhibits geometric scaling and scaling violations by the diffusion term. For dipole sizes larger than 1/Q s (x), the scattering amplitude saturates to one. The fit involves three parameters: the proton radius R, the value x 0 of x at which the saturation scale Q s equals 1GeV, and the logarithmic derivative of the saturation momentum λ. The value of λ extracted from the fit turns out to be consistent with a recent calculation using the next-to-leading order BFKL formalism.

We show that the evolution equations in QCD predict geometric scaling for quark and gluon distribution functions in a large kinematical window, which extends above the saturation scale up to momenta Q 2 of order 100 GeV 2 . For Q 2 < Q 2 s , with Q s the saturation momentum, this is the scaling predicted by the Colour Glass Condensate and by phenomenological saturation models., we show that the solution to the BFKL equation shows approximate scaling, with the scale set by Q s . At larger Q 2 , this solution does not scale any longer. We argue that for the intermediate values of Q 2 where we find scaling, the BFKL rather than the double logarithmic approximation to the DGLAP equation properly describes the dynamics. We consider both fixed and running couplings, with the scale for running set by the saturation momentum. The anomalous dimension which characterizes the approach of the gluon distribution function towards saturation is found to be close to, but lower than, one half.