  The concept of superbandwidth refers to the fact that a band-limited signal
can exhibit, locally, an increase of its bandwidth, i.e., an effective
bandwidth greater than that predicted by its Fourier transform. In this work,
we study the propagation of superbandwidth laser pulses in a dispersive medium,
characterized by the group velocity dispersion. In particular, two important
results arise from the analysis of the instantaneous frequency of the pulse
obtained through the Wigner function distribution: First, it can be observed
local oscillations of the electric field which are beyond the Fourier spectrum
of the incoming pulse. Second, for a range of values of the pulse synthesis
parameters, surprisingly, the dynamics of the instantaneous frequency within
certain temporal regions, corresponds to that of a pulse propagating in a
medium with a group velocity dispersion of opposite sign. This phenomenon is
intrinsic to the special characteristics of the pulse and not to the dispersive
properties of the medium.
