  Dispersion effects induce new instabilities and dynamics in the weakly
nonlinear description of light propagation in fiber Bragg gratings. A new
family of dispersive localized pulses that propagate with the group velocity is
numerically found and its stability is also analyzed. The unavoidable different
asymptotic order of transport and dispersion effects plays a crucial role in
the determination of these localized states. These results are also interesting
from the point of view of general pattern formation since this asymptotic
imbalance is a generic situation in any transport dominated (i.e., nonzero
group velocity) spatially extended system.
