In this paper, we have investigated the effects of well numbers, maximum refractive index variation Δn0, saturable nonlinearity β and soliton amplitude N on behavior of a spatial soliton propagating through a waveguide having a parabolic rectangular index profile. The aim of this work is to find the optimal values for these parameters in order to achieve the best soliton behavior. We found that the best system is one with N = 3, β = 0.4 and well number = 20. Knowing these optimal values helps experimenters to select the optimal system. In addition, to study the behavior of the propagating soliton, localization of the soliton was investigated under variations of a variety of the above-mentioned quantities. Our results show that localization of a soliton for the propagation distance z < 10, under increase of maximum index variation Δn0 increases, while it decreases under increase of well numbers and saturable nonlinearity β. On the other hand, for propagation distance z > 10, the effective width (Weff) of the soliton shows an oscillatory behavior. The amplitude of Weff oscillations with increasing well number decreases, and the soliton becomes more localized. In contrast, with increase of β, Weff oscillations increase.
