We study numerically the small-$x$ behavior of the nuclear gluon distribution function $G^A(x,Q^2)$ in the next-to-leading order (NLO) approximation of the Gribov-Levin-Ryskin-Mueller-Qiu, Zhu-Ruan-Shen (GLR-MQ-ZRS) nonlinear equation and quantify the impact of gluon recombination in the kinematic range $x\le {10}^{-2}$ and $Q^2\ge 5{\text{GeV}}^2$. The results are comparable to the Rausch-Guzey-Klasen (RGK) [J. Rausch, V. Guzey, and M. Klasen, Phys. Rev. D 107, 054003 (2023)] nuclear gluon distributions and the nCTEQ15 parametrization at the corresponding $Q^2$ values. Using the solutions of $G^A(x,Q^2)$ in the framework of the nonlinear GLR-MQ-ZRS evolution equation, both the linear and nonlinear behaviors of the charm structure functions of nuclei per nucleon, $F_2^{c\overline{c}-A}(x,Q^2)$ and $F_L^{c\overline{c}-A}(x,Q^2)$, are considered. The results reveal that nonlinear corrections play an important role in the charm nuclear reduced cross sections at small $x$ and low $Q^2$ values. The computed results are compared with experimental data from the H1 and ZEUS Collaborations.

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• Parton distribution functions
• Perturbative QCD
• QCD in nuclear reactions
• QCD phenomenology
• Quantum chromodynamics