We study the dynamics of short optical pulses in a real system with periodically distributed dispersion and the nonlinearity is governed by the higher order nonlinear Schr?dinger equation (HNLSE) with linear and nonlinear gain (loss). Under specific parametric circumstances, where the dark and bright solitary waves are combined, a set of entirely new types of solitary waves with nonlinear chirp have emerged. For a properly intense optical pulse in the combined solitary waves, the binding of the bright and dark solitary waves is very strong. It is seen that by numerical simulation, these pooled types of solitary-like solutions show a high degree of stability while propagating over an extremely long distance in the considering system, even in the presence of a high degree of perturbation of the amplitude and white noise. All constraint relations on the physical parameters are explicitly shown to be related to the development and to the dynamical study of the chirped solitary like solution in the considering medium.