Structure function of the nucleus in the perturbative QCD with $N_c\to\infty$ (BFKL pomeron fan diagrams)

Equation for the sum of BFKL pomeron fan diagrams is rederived by direct summation and solved numerically for rapidities $y\leq 50$. At high rapidities $y>20$ the resulting cross-sections for the scattering of a $q\bar q$ pair on the nucleus cease to depend on its transverse dimension and tend to a constant limit ($\sim 0.34 R_A^2$ for the transverse polarization). Thus the unitarity is restored and the singularity in the $j$ plane seems to be reduced to a simple pole at $j=1$. The nuclear structure function correspondingly saturates at small $x$, the limiting function resulting proportional to $Q^2$. The found gluon density has a form of a soliton wave in the $\log k$ space: its form is Gaussian, independent of rapidity, the center moving towards higher $\log k$ with a constant velocity as rapidity increases