This study reveals the dynamics of short optical pulses in nonlinear media. Then, for the survival of different types of solitary waves in the nonlinear medium, the constraint relations to the physical parameters and chirps associated with each of the solitary waves are explicitly shown. We authenticate numerically all those obtained from the analytical method and show the chirping effect is saturative in nature and can be managed by changing coefficients of inter-modal dispersion, stimulated Raman scattering (SRS), and self-steepening effect. We also verify the more operative condition of intermodal dispersion.