Femtosecond sliding self-pumping and self-cleaning effects in nonlinear dynamics of the higher-order induced modulational instability under the strong Raman self-scattering

We clarify an analytical approach in the theory of modulational instability developed in the framework of the nonautonomous nonlinear Schrödinger equation model taking into account three mathematical models of the Raman self-scattering effect and arbitrary orders of the even group velocity dispersion. We reveal important analogies and significant distinctions between the higher-order induced modulational instability and the internal dynamics of the higher-order N-soliton bound states. We demonstrate that periodic interference splitting onto two or more well-separated wave components and the numbers of split rogue wave-like peaks are determined by the total number of solitons accumulated in the initial wave profile. Our direct computer experiments reveal the crucial role of the sliding pump effect at the nonlinear stage of the higher-order induced modulational instability giving rise to the soliton self-cleaning effect.