  We report a numerical study on generation and stability of parabolic pulses
during their propagation through highly nonlinear specialty optical fibers.
Here, we have generated a parabolic pulse at 2.1 $\mu$m wavelength from a
Gaussian input pulse with 1.9 ps FWHM and 75 W peak power after travelling
through only 20 cm length of a chalcogenide glass based microstructured optical
fiber (MOF). Dependence on input pulse shapes towards most efficient conversion
into self similar states is reported. The stability in terms of any deviation
from dissipative self-similar nature of such pulses has been analyzed by
introducing a variable longitudinal loss profile within the spectral loss
window of the MOF, and detailed pulse shapes are captured. Moreover, three
different dispersion regimes of propagation have been considered to study the
suitability to support most stable propagation of the pulse.
