When an optical pulse is launched into a fiber with anomalous chromatic dispersion so that the pulse parameters do not exactly match those of a soliton, the pulse will evolve (within some propagation distance in the fiber) into a soliton pulse and some temporally spreading background. The latter is called a dispersive wave, because it is spreading due to the effect of group delay dispersion, and this is not compensated by the fiber nonlinearity, since the peak power is too low. The closer the parameters of the initial pulse are to the parameters of a soliton, the higher is the percentage of the pulse energy which ends up in the soliton rather than in the dispersive wave.
A dispersive wave can also be formed when the soliton is disturbed in some way, e.g. by a localized loss in the fiber (causing a deviation from the soliton condition by suddenly reducing the pulse energy) or by the transition into a fiber with modified parameters. Similar effects occur for quasi-soliton pulses circulating in the resonator of a mode-locked laser, where dispersion and nonlinearity usually occur in discrete packages rather than smoothly distributed as in a fiber. The circulating soliton is thus subject to periodically occurring disturbances, which couple the soliton to the copropagating dispersive wave. This also happens in a mode-locked fiber laser, even if its laser resonator is made from fibers only, since the pulse energy usually undergoes large changes in each round trip and also because fibers with different dispersion and/or nonlinearity may be used within the resonator. The periodic disturbance of the circulating soliton can result in the formation of Kelly sidebands.