The authors investigate the soliton transmission of optical pulses in nonlinear inhomogeneous graded-refractive-index fibers (biquadratic profile). Avoiding the linear fashion approximation, the radial dependence of the field is treated. The obtained solutions are parametrically controlled in such a manner that both the light and dark solitons exist in both normal and anomalous dispersion regions. The controlling parameters affect the power required to achieve soliton propagation, the bit rate, and the group velocity.