  In this paper we developed approach based on the BFKL evolution in $\ln\Lb Q^2\Rb$. We show that the simplest diffusion approximation with running QCD coupling is able to describe the HERA experimental data on the deep inelastic structure function with good $\chi^2/d.o.f. \approx 1.3$. From our description of the experimental data we learned several lessons; (i) the non-perturbative physics at long distances started to show up at $Q^2 = 0.25\,GeV^2$; (ii) the scattering amplitude at $Q^2 = 0.25\,GeV^2$ cannot be written as sum of soft Pomeron and the secondary Reggeon but the Pomeron interactions should be taken into account; (iii) the Pomeron interactions can be reduced to the enhanced diagrams and, therefore, we do not see any needs for the shadowing corrections at HERA energies; and (iv) we demonstrated that the shadowing correction could be sizable at higher than HERA energies without any contradiction with our initial conditions. 
BFKL equation with running QCD coupling and HERA data