  We suggest a modified form of a unitarized BFKL equation imposing the
so-called kinematic constraint on the gluon evolution in multi-Regge
kinematics. The underlying nonlinear effects on the gluon evolution are
investigated by solving the unitarized BFKL equation analytically. We obtain an
equation of the critical boundary between dilute and dense partonic system,
following a new differential geometric approach and sketch a phenomenological
insight on geometrical scaling. Later we illustrate the phenomenological
implication of our solution for unintegrated gluon distribution $f(x,k_T^2)$
towards exploring high precision HERA DIS data by theoretical prediction of
proton structure functions ($F_2$ and $F_L$) as well as double differential
reduced cross section $(\sigma_r)$. The validity of our theory in the low $Q^2$
transition region is established by studying virtual photon-proton cross
section in light of HERA data.
