Peregrine comb: multiple compression points for Peregrine rogue waves in periodically modulated nonlinear Schr{ö}dinger equations

Abstract

It is shown that sufficiently large periodic modulations in the coefficients of a nonlinear Schr{ö}dinger equation can drastically impact the spatial shape of the Peregrine soliton solutions: they can develop multiple compression points of the same amplitude, rather than only a single one, as in the spatially homogeneous focusing nonlinear Schr{ö}dinger equation. The additional compression points are generated in pairs forming a comb-like structure. The number of additional pairs depends on the amplitude of the modulation but not on its wavelength, which controls their separation distance. The dynamics and characteristics of these generalized Peregrine soliton are analytically described in the case of a completely integrable modulation. A numerical investigation shows that their main properties persist in nonintegrable situations, where no exact analytical expression of the generalized Peregrine soliton is available. Our predictions are in good agreement with numerical findings for an interesting specific case of an experimentally realizable periodically dispersion modulated photonic crystal fiber. Our results therefore pave the way for the experimental control and manipulation of the formation of generalized Peregrine rogue waves in the wide class of physical systems modeled by the nonlinear Schr{ö}dinger equation.

References in corpus (4)

• Instabilities, breathers and rogue waves in optics
• Harnessing and control of optical rogue waves in supercontinuum generation
• Breather-like solitons extracted from the Peregrine rogue wave
• Modulational instability in dispersion-kicked optical fibers

Cited by in corpus (6)

• Breather transition dynamics, Peregrine combs/walls and modulation instability in a variable-coefficient nonlinear Schrödinger equation with higher-order effects
• Symmetric and asymmetric optical multi-peak solitons on a continuous wave background in the femtosecond regime
• Superposed nonlinear waves in coherently coupled Bose-Einstein condensates
• Dispersion Managed Generation of Peregrine Solitons and Kuznetsov-Ma Breather in an Optical Fiber
• Nonlinear bandgap transmission by discrete rogue waves induced in a pendulum chain
• Modulation instability and controllable rogue waves with multiple compression points for periodically modulated coupled Hirota equations