  One-dimensional defect photonic crystal (Bragg waveguide) is studied from the
viewpoint of the slow light problem. The calculations are presented showing
that in the TiO$_2$/SiO$_2$-based Bragg waveguide one can obtain the group
index of $\sim$ 1000 and spatial decay length of $\sim$ 3 mm for a
nanosecond-scale pulse. Distortion of the pulse due to the group index
dispersion proves to be acceptable for the relative pulse delay not exceeding
10. We also analyze propagation of the light pulse in the Bragg waveguide with
a quantum well inside and provide arguments showing possibility of reaching the
group index of $\sim$ 10000. To the best of our knowledge, analysis of pulse
propagation in a Bragg waveguide in connection with the slow light problem has
not been performed so far. We will still much appreciate any information about
such studies, if any.
