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In this work we have solved the nonlinear GLR-MQ evolution equation uptonext-to-leading order (NLO) by considering NLO terms of the gluon-gluonsplitting functions and running coupling constant $\alpha_s(Q^2)$. Here, wehave incorporated a Regge-like behaviour of gluon distribution in order toobtain a solution of the GLR-MQ equation in the range of $5 GeV^2 \leq Q^2 \leq25 GeV^2$. We have studied the $Q^2$ evolution of the gluon distributionfunction $G(x,Q^2)$ and its nonlinear effects at small-x. It can be observedfrom our analysis that the nonlinearities increase with decrease in thecorrelation radius R of two interacting gluons, as expected. We have comparedour result of $G(x,Q^2)$ as $Q^2$ increases and x decreases, for two differentvalues of R, viz. R= 2 $GeV^{-1}$ and 5 $GeV^{-1}$. We have also checked thesensitivity of the Regge intercept $\lambda_G$ on our results. We compare ourcomputed results with those obtained by the global analysis to partondistribution functions (PDFs) by various collaborations where LHC data havebeen included viz. PDF4LHC15, NNPDF3.0, ABM12 and CT14. Besides we have alsoshown comparison of our results with HERA PDF data viz. HERAPDF15.

Nonlinear effects in gluon distribution predicted by GLR-MQ evolution equation at next-to-leading order in LHC data