QCD predictions for the behavior of the gluon distribution at small x

The very-small-x behavior of the gluon distribution in a proton is obtained by solving the Lipatov equation with the nonlinear shadowing term incorporated. We find, with decreasing x, the emergence of an x-λ behavior and he eventual taming of this singular behavior by the shadowing term. We compare our dynamically generated gluon distribution with (i) the results of a recent next-to-leading order QCD structure function analysis which incorporated both a singular x-1/2 behavior and shadowing corrections, and (ii) the double-leading-logarithm approximation. We formulate the semiclassical approximation of the Lipatov equation, with and without shadowing contributions, in order to compare with earlier analyses based on this approximation