  Nonlinear QCD evolution equations are essential tools in understanding the
saturation of partons at small Bjorken $x_{\rm B}$, as they are supposed to
restore an upper bound of unitarity for the cross section of high energy
scattering. In this paper, we present an analytical solution of
Balitsky-Kovchegov (BK) equation using the homogeneous balance method. The
obtained analytical solution is similar to the solution of a traveling wave. By
matching the gluon distribution in the dilute region which is determined from
the global analysis of experimental data (CT14 analysis), we get a definitive
solution of the dipole-proton forward scattering amplitude in the momentum
space. Based on the acquired scattering amplitude and the behavior of geometric
scaling, we present also a new estimated saturation scale $Q_s^2(x)$.
