Rogue wave spectra of the Kundu-Eckhaus equation

Abstract

In this paper we analyze the rogue wave spectra of the Kundu-Eckhaus equation (KEE). We compare our findings with their nonlinear Schrödinger equation (NLSE) analogs and show that the spectra of the individual rogue waves significantly differ from their NLSE analogs. A remarkable difference is the one-sided development of the triangular spectrum before the rogue wave becomes evident in time. Also we show that increasing the skewness of the rogue wave results in increased asymmetry in the triangular Fourier spectra. Additionally, the triangular spectra of the rogue waves of the KEE begin to develop at earlier stages of the their development compared to their NLSE analogs, especially for larger skew angles. This feature may be used to enhance the early warning times of the rogue waves. However we show that in a chaotic wavefield with many spectral components the triangular spectra remains as the main attribute as a universal feature of the typical wavefields produced through modulation instability and characteristic features of the KEE's analtical rogue wave spectra may be suppressed in a realistic chaotic wavefield.

Rogue quantum harmonic oscillations

“…Checking the figure, it is possible to conclude that increase in σ leads to higher probability for wavefunction to be in the intervals of |ψ| ≈ [0.0 − 0.7] and |ψ| ≈ [1.7 − 5.0], however the probability of wavefunction to be in the interval of |ψ| ≈ [0.7 − 1.7] decreases as σ increases, due to stronger interactions leading to more energy leakage to sideband wavenumbers. A similar result can also be seen in [28] for the Kundu-Eckhaus equation which has quintic nonlinearity effect.…”

A Generalized Kundu-Eckhaus Equation With An Extra-Dispersion: Pulses Configuration

“…We mention, rhombus, complex chirped and pulses-cascade are new. Also it is found that the pulse spectrum is chaotic which agree with the results found in [34]. Relevant works on nonlocal NLSE were carried in [35,36] The method used here is compared with the known methods, in the literature, as in what follows:…”

Rogue waves and W-shaped solitons in the multiple self-induced transparency system

“…2(b). The analogous phenomena produced by the higher-order effects have been comprehensively studied for rogue waves in the Hirota equation [24], Sasa-Satsuma equation [25] and Kundu-Eckhaus equation [36,39], while for the coupled system without any higher-order terms they have been rarely reported.…”