  We propose a new semi-analytical model, describing the bandwidth evolution of
pulses propagating in dispersion managed (DM) transmission systems using
multimodal graded-index fibers (GRIN) with parabolic index. The model also
applies to monomodal fiber DM systems, representing the limit case where beam
self-imaging vanishes. The model is successfully compared with the direct
integration of the (1+1)D nonlinear Schr\"odinger equation for parabolic GRIN
fibers, and to experimental results performed by using the transmission of
femtosecond pulses over a 5 m span of GRIN fiber. At the high pulse powers that
are possible in multimodal fibers, the pulse bandwidth variations produced by
the interplay of cumulated dispersion and self-phase modulation can become the
most detrimental effect, if not properly managed. The analytical model,
numerical and experimental results all point to the existence of an optimal
amount of chromatic dispersion, that must be provided to the input pulse, for
obtaining a periodic evolution of its bandwidth. Results are promising for the
generation of spatio-temporal DM solitons in parabolic GRIN fibers, where the
stable, periodic time-bandwidth behaviour that was already observed in
monomodal systems is added to the characteristic spatial beam self-imaging.
