Influence of cnoidal wave on optical soliton run

We studied the influence of cnoidal wave on optical soliton run. We found that cnoidal wave only perturb the amplitude and velocity of soliton when the amplitude of cnoidal wave is small enough to satisfy the condictions of adiabatic perturbation. We further found that the influences of cnoidal wave on the amplitude and velocity of soliton are periodic when other factors are ignored.