  We present a phenomenological study of the small-x behaviour of gluon
distribution function $G(x,Q^2)$ at next-to-leading order (NLO) and
next-to-next-to-leading order(NNLO) in light of the nonlinear
Gribov-Ryskin-Levin-Mueller-Qiu (GLR-MQ)evolution equation by keeping the
transverse size of the gluons ($\sim 1/Q$) fixed. We consider the NLO and NNLO
corrections, of the gluon-gluon spitting function $P_{gg} (z)$ and strong
coupling constant $\alpha_s (Q^2)$. We have suggested semi-analytical solutions
based on Regge like ansatz of gluon density $G(x,Q^2)$, which are supposed to
be valid in the moderate range of photon virtuality$(Q^2)$ and at small Bjorken
variable$(x)$. The study of the effects of nonlinearities that arise due to
gluon recombination effects at small-x is very interesting, which eventually
tames down the unusual growth of gluon densities towards small-x as predicted
by the linear DGLAP evolution equation.
