Abstract
The super rogue wave dynamics in optical fibers are investigated within the framework of a generalized nonlinear Schrödinger equation containing group-velocity dispersion, Kerr and quintic nonlinearity, and self-steepening effect. In terms of the explicit rogue wave solutions up to the third order, we show that, for a rogue wave solution of order n, it can be shaped up as a single super rogue wave state with its peak amplitude 2n+1 times the background level, which results from the superposition of n(n+1)/2 Peregrine solitons. Particularly, we demonstrate that these super rogue waves involve a frequency chirp that is also localized in both time and space. The robustness of the super chirped rogue waves against white-noise perturbations as well as the possibility of generating them in a turbulent field is numerically confirmed, which anticipates their accessibility to experimental observation.
Highlights
As an optical counterpart of the infamous oceanic rogue waves that have been held responsible for numerous marine misfortunes [1], optical rogue waves [2] are attracting burgeoning interest of research on both theoretical and experimental sides [3, 4], due to their potential applications and their comparative ease to create and capture in a laboratorial environment [5]
Rogue waves have been successfully observed in a number of optical settings such as optical fibers [13], mode-locked lasers [14], microresonators [15], and photorefractive ferroelectrics [16], not to mention those observed in filamentation [17], beam speckles [18], caustics [19], and integrable turbulence [20]
In terms of the explicit rogue wave solutions up to the third order, we show that, for a rogue wave solution of order n, it can be shaped up as a single super rogue wave state with its peak amplitude 2n + 1 times the background level, which arises from the superposition of n(n + 1)/2 Peregrine solitons
Summary
As an optical counterpart of the infamous oceanic rogue waves that have been held responsible for numerous marine misfortunes [1], optical rogue waves [2] are attracting burgeoning interest of research on both theoretical and experimental sides [3, 4], due to their potential applications and their comparative ease to create and capture in a laboratorial environment [5]. A typical example is the Peregrine soliton, which was first discovered in 1983 by Peregrine as the fundamental rational solution to the celebrated nonlinear Schrödinger (NLS) equation [22] It is built on a finite continuous background, reaching a climax three times the background height followed by two deep troughs, and is not a genuine ‘soliton’. We investigate the chirped version of higher-order rogue waves, termed super chirped rogue waves for their super high peak amplitude, within the framework of a generalized NLS equation that contains the group-velocity dispersion (GVD), the Kerr and quintic nonlinearity, and the self-steepening effect [42]. The stability of the super chirped rogue waves as well as the possibility to generate them in a turbulent field is numerically confirmed, which anticipates an accessibility to experimental observation
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