  We present a modification of the DGLAP improved saturation model with respect
to the nonlinear correction (NLC). The GLR-MQ improved saturation model is
considered by employing the parametrization of proton structure function due to
the Laplace transforms method, which preserves its behavior success in the low
and high $Q^{2}$ regions. We show that the geometric scaling holds for the
GLR-MQ improved model in a wide kinematic region $rQ_{s}$. These results are
comparable with other models in a wide kinematic region $rQ_{s}$. The behavior
of the dipole cross sections, with respect to the GLR-MQ improved saturation
model, are comparable with the Color Glass Condensate (CGC) model. The model
describes the dipole cross sections in the inclusive and diffractive processes.
We also compare the nonlinear corrections to the impact-parameter dependent
saturation (IP-Sat) model with the impact-parameter dependent color glass
condensate (b-CGC) dipole model. Finally, we consider the linear and nonlinear
corrections to the IP Non-Sat model. These results provide a benchmark for
further investigation of QCD at small $x$ in future experiments such as the
Large Hadron Collider and Future Circular Collider projects.
