Peregrine Solitons Beyond the Threefold Limit and Their Two-Soliton Interactions

Abstract

Within the coupled Fokas-Lenells equations framework, we show explicitly that, in contrast to the expected threefold-amplitude magnification, Peregrine solitons can reach a peak amplitude as high as 5 times the background level. Besides, the interaction of two such anomalous Peregrine solitons can generate a spikelike rogue wave of extremely high peak amplitude, depending on the parameters used. We numerically confirm that the Peregrine soliton beyond the threefold limit can be reproduced from either a deterministic initial profile or a chaotic background field, hence anticipating the feasibility of its experimental observation.

Super chirped rogue waves in optical fibers

“…As it can mimic realistic extreme wave events, the Peregrine soliton has become a popular prototype of rogue waves in many areas [5,23]. Recent studies reveal that Peregrine solitons are universal solutions of majority of integrable models [24][25][26], not peculiar to the NLS equation, and have many interesting variants of emergence such as dark Peregrine solitons [27], anomalous Peregrine solitons [28], and chirped Peregrine solitons [29]. Of particular interest is the chirped Peregrine soliton, which can possess an extra doubly localized chirp while keeping the intensity features of the original Peregrine soliton.…”

General rogue wave solutions of the coupled Fokas–Lenells equations and non-recursive Darboux transformation

“…We point out that the fundamental solution (4.9) thus obtained can reduce, with considerable simplifications, to that presented in [41]. This solution can represent an anomaly of Peregrine soliton creation by which we mean the peak amplitude can go beyond the threefold amplitude limit, as shown in figure 4, where the fourfold-amplitude Peregrine soliton and its doublet state are exhibited.…”

“…Likewise, by anomalous Peregrine soliton we mean a complex fundamental rational solution which consists of quadratic polynomials featured by the Peregrine solitons, while having a peak amplitude beyond the threefold amplitude limit of the usual Peregrine solitons [27,29,62]. Such a Peregrine soliton anomaly was first reported in [41] and was shown to be able to be excited numerically from a turbulent field caused by noise. In this article, we showed further, on an analytical level, that the enforcement amplitude factor can be unexpectedly large (e.g.…”

Peregrine Solitons on a Periodic Background in the Vector Cubic-Quintic Nonlinear Schrödinger Equation

“…Its importance and universality have been confirmed by a succession of well-designed experiments, with physical settings spanning from the water-wave tanks [26] to optical fibers [21,27], and from the deep ocean [28] to plasmas [29]. Moreover, in a multicomponent (or vector) nonlinear system, some variants of Peregrine solitons such as dark Peregrine solitons [30] and anomalous Peregrine solitons [31,32] have come to light, opening new perspectives on the versatility of Peregrine solitons as an essential prototype in rogue wave science. Here, in a broad sense, we still term the fundamental rogue waves in a multicomponent system Peregrine solitons or Peregrine solitary waves, provided that they inherit the basic wave features of the Peregrine soliton in the original NLS equation [33,34].…”