  We determined the effects of the first nonlinear corrections to the gluon
distribution using the solution of the QCD nonlinear
Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (NLDGLAP) evolution equation at
small x. By using a Laplace-transform technique, the behavior of the gluon
distribution is obtained by solving the Gribov, Levin, Ryskin, Mueller and Qiu
(GLR-MQ) evolution equation with the nonlinear shadowing term incorporated. We
show that the strong rise that is corresponding to the linear QCD evolution
equations at small x can be tamed by screening effects. Consequently, the
nonlinear effects for the gluon distributions are calculated and compared with
the results for the integrated gluon density from the Balitsky-Kovchegov (BK)
equation. The resulting analytic expression allows us to predict the shadowing
correction to the logarithmic derivative $F_{2}(x,Q^{2})$ with respect to $ln
Q^{2}$ and to compare the results with H1 data and a QCD analysis fit.
