Random evolution and coherence degradation of a high-order optical soliton train in the presence of noise

The intrinsic evolution of a high-order soliton described by the nonlinear Schrödinger equation is initiated by a self-four-wave mixing effect (or modulational instability) and recurs neatly every soliton period. We show that when there is noise such as amplified spontaneous emission, however, a high-order soliton evolves randomly and independently and is distorted because the evolution is initiated by noise. Thus the time and the frequency coherence of a soliton pulse train are both greatly degraded.