Parabolic optical pulses with their characteristic linear chirp have profound importance in nonlinear optics as they have immense capability to withstand strong nonlinearity which prevents wave-breaking. Moreover, their evolution is self-similar, hence they are typically known as similaritons. Such wave-breaking free parabolic similaritons are widely applicable in all-fiber based devices like, high energy fiber laser sources, bio/chemical sensors, supercontinuum generators, bio-medical imaging and non-invasive surgery tools and so on. To date, theoretical and experimental formation of PPs have been reported for both active and passive optical fibers where PPs are asymptotic solutions of nonlinear Schrodinger equation (NLSE) . It is clearly reported that PPs in active fibers are highly stable and evolve self-similarly over longer propagation distance whereas, passive formation of PPs are a mere intermediate transient state of propagation and with further evolution it becomes unstable . In this context, another two types of similaritons (bright and dark) have been reported which are exact solutions of NLSE and found to propagate self-consistently against their asymptotic counterpart . While encountering the stability issue of PPs in passive medium, it has been seen that high values of dispersion are being detrimental leading to wave-breaking. Hence some dispersion managed schemes have reported that effectively suppresses the excessive dispersive phase accumulation and stabilize the pulse over a few meters . In this paper, we report formation and stable propagation of PPs over few hundreds of meters through a soft glass based tapered Bragg fiber. Instead of employing any dispersion managing technique, we simply have exploited the self-consistent nature of a bright (sechyperbolic) and dark (tanhyperbolic) similaritons and formed parabolic pulses in a decreasing dispersion profile. © 2018 OSA - The Optical Society. All rights reserved.