We investigate the evolution of Gaussian input conditions in fibre links wi
th dispersion management. Gaussian pulses, which do not exactly match any s
ystem eigenmode, suffer from both initial transient evolutions and asymptot
ic slow oscillations. By means of chirped Hermite-Gauss bases, we analytica
lly characterize and discuss these pulse dynamics in terms of interplay amo
ng the different Hermite-Gauss modes.