  I study the incorporation of renormalization group (RG) improved BFKL kernels
in the Balitsky-Kovchegov (BK) equation which describes parton saturation. The
RG improvement takes into account important parts of the next-to-leading and
higher order logarithmic corrections to the kernel. The traveling wave front
method for analyzing the BK equation is generalized to deal with RG-resummed
kernels, restricting to the interesting case of fixed QCD coupling. The results
show that the higher order corrections suppress the rapid increase of the
saturation scale with increasing rapidity. I also perform a "diffusive"
differential equation approximation, which illustrates that some important
qualitative properties of the kernel change when including RG corrections.
