High-order solitons and the modulational instability

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Abstract
The connection between the modulational instability (MI) and the evolution of a higher-order soliton is described. The amplitude ripples that appear on the higher-order soliton can be regarded as a MI. A perturbation theory for higher-order solitons is developed to show differences between the cw MI and the pulsed MI. Initiation of the MI ripples on the soliton pulse is produced by MI amplification of the Fourier components of maximum gain. This phenomenon is corroborated by the study of the breakup of super-Gaussian pulses. Higher-order effects such as the third-order dispersion, shock, and the self-induced Raman effect in a nonlinear Schrödinger equation (NLS) are studied from the point of view of the MI process. It is shown that the Raman effect can enhance generation of the ripple because the parametric noise can build up faster than by MI alone as described by the NLS without perturbations.