  The possibility of tailoring the guidance properties of optical fibers along
the same direction as the evolution of the optical field allows to explore new
directions in nonlinear fiber optics. The new degree of freedom offered by
axially-varying optical fibers enables to revisit well-established nonlinear
phenomena, and even to discover novel short pulse nonlinear dynamics. Here we
study the impact of meter-scale longitudinal variations of group velocity
dispersion on the propagation of bright solitons and on their associated
dispersive waves. We show that the longitudinal tailoring of fiber properties
allows to observe experimentally unique dispersive waves dynamics, such as the
emission of cascaded, multiple or polychromatic dispersive waves.
