Nonlinear terms from GLR-MQ evolution

We show that the saturation exponent is more effective than the hard pomeron exponent in the nonlinear terms for the GLR-MQ evolution equations. For the gluon distribution the nonlinear terms are found to play an increasingly important role than the singlet distribution. The nonlinear corrections for the singlet and gluon distributions are important in a limited range of $Q^2$ and are independent of the upward and downward evolution. This allows us to single out the region where the nonlinear corrections may provide evidence for recombination. We numerically study the nonlinear terms for nuclear singlet and gluon distributions and quantify the impact of gluon recombination in a wide range of $Q^2$. This analysis indicates that the nonlinear effects are most pronounced for heavy nuclei and are sizable at $2{\lesssim}Q^2{\lesssim}20~\mathrm{GeV}^2$ for light and heavy nuclei.