Rogue waves of the Sasa-Satsuma equation in a chaotic wave field

Soto-Crespo, J. M.; Devine, Natasha; Hoffmann, Norbert; Akhmediev, Nail

doi:10.1103/physreve.90.032902

Cited by 53 publications

(35 citation statements)

References 41 publications

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“…Therefore their results can be predicted for a given initial condition. Therefore compared to the completely unpredictable 'stochastic' processes, the processes described in the frame of the KEE can be described as 'chaotic' [14]. The term 'chaotic' is used in this setting throughout this paper.…”

Section: Spectra Of the Chaotic Wave Fieldmentioning

confidence: 99%

Rogue wave spectra of the Kundu-Eckhaus equation

Bayındır

2016

Phys. Rev. E

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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.

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Section: Spectra Of the Chaotic Wave Fieldmentioning

confidence: 99%

Rogue wave spectra of the Kundu-Eckhaus equation

Bayındır

2016

Phys. Rev. E

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“…Nevertheless, the MI often exhibits some interesting features when the additional physical effects are taken into consideration, such as cross-phase modulation [10, 11], higher-order perturbation terms [12], etc. Thus, it is important to study the rogue wave property induced by the features of MI growth rate distribution.Recent studies demonstrate that rogue wave can exhibit structural diversity beyond the reach of the standard NLSE in presence of higher-order effects [13][14][15][16][17][18][19][20][21][22][23][24]. However, to our knowledge, less attention has been paid to analyzing rogue wave property in combination with the distribution characteristic of corresponding MI growth rate.…”

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confidence: 99%

State transition induced by higher-order effects and background frequency

et al. 2015

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State transition between the Peregrine rogue wave and w-shaped traveling wave induced by higherorder effects and background frequency is studied. We find that this intriguing transition, described by an exact explicit rational solution, is consistent with the modulation instability (MI) analysis that involves MI region and stability region in low perturbation frequency region. In particular, the link between the MI growth rate and transition characteristic analytically demonstrates that, the size characteristic of transition is positively associated with the reciprocal of zero-frequency growth rate. Further, we investigate the case for nonlinear interplay of multi-localized waves. It is interesting that the interaction of second-order waves in stability region features a line structure, rather than an elastic interaction between two w-shaped traveling waves. [7,8] of weakly modulated plane wave. More specifically, rogue waves exist only in the MI subregion where the instability frequency band is close to the vanishing frequency [9]. In this regard, rogue wave has a consistent structure in the standard nonlinear Schrödinger equation (NLSE) where the MI characteristic remains invariant in nature. Nevertheless, the MI often exhibits some interesting features when the additional physical effects are taken into consideration, such as cross-phase modulation [10, 11], higher-order perturbation terms [12], etc. Thus, it is important to study the rogue wave property induced by the features of MI growth rate distribution.Recent studies demonstrate that rogue wave can exhibit structural diversity beyond the reach of the standard NLSE in presence of higher-order effects [13][14][15][16][17][18][19][20][21][22][23][24]. However, to our knowledge, less attention has been paid to analyzing rogue wave property in combination with the distribution characteristic of corresponding MI growth rate. Here we find that, with some higher-order perturbation terms (the third-order dispersion and delayed nonlinear response term), the MI growth rate shows a non-uniform distribution characteristic in low perturbation frequency region, in particular, it opens up a stability region as background frequency changes (see Fig. 1). Thus we anticipate that there will be some interesting physical properties as a rogue wave evolves and approaches the stability region.As a starting point, we address the problem via a completely integrable higher-order NLSE-the Hirota equa- * Electronic address: zyyang@nwu.edu.cn † Electronic address: zhaolichen3@163.com tion (HE) [25]-which involves the higher-order perturbation effects. In dimensionless form, the HE readswhere z is the propagation variable, t is the retarded time in a moving frame with the group velocity, and E(t, z) is the slowly varying envelope of the wave field. The real parameter β is introduced to be responsible for the thirdorder dispersion and delayed nonlinear response term, respectively. If β = 0, it reduces to the standard NLSE. The existence of rogue waves in the HE has been recently dem...

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“…The connection between baseband MI and the occurrence of RWs has been established for several coupled nonlinear systems, e.g., coupled NLSEs, coupled derivative NLSEs, and long wave‐short wave resonance model . While previous works reported on the emergence of RWs from perturbations as a random noise , it proves valuable to investigate the evolution of specific modes directly. We focus on the evolution of wavy disturbances on a plane wave background, where the initial condition becomes

\begin{matrix} true \\ right A ((), x, 0) & = & left ([], 1 + 0.05 prefixexp ((), i K x)) A_{0} ((), x, 0), \\ right B ((), x, 0) & = & left ([], 1 + 0.05 prefixexp ((), i K x)) B_{0} ((), x, 0), \end{matrix}

where A 0 and B 0 are given in Eq.…”

Section: Numerical Study On Wavy Perturbationsmentioning

confidence: 99%

“…While similar approaches might have been adopted in earlier works , we also exhibit the connection between the instability gain spectrum and RWs by following the time evolution of a plane wave subjected to a disturbance of a specified frequency. With information from the MI gain spectrum, further quantitative trends can be deduced.…”

Section: Introductionmentioning

confidence: 99%

Rogue Waves for an Alternative System of Coupled Hirota Equations: Structural Robustness and Modulation Instabilities

Chan

Chow

2017

Stud Appl Math

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The Hirota system consists of two coupled, third‐order partial differential equations with cubic nonlinearities. Rogue wave (RW) modes for such coupled Hirota equations different from those usually considered in the literature are derived by the bilinear method. RWs exist in the defocusing regime (dispersion and nonlinearities of different signs), with an existence criterion closely related to the condition for baseband modulation instability (MI). This connection is examined further through numerical simulations. RW‐like structures can emerge from a plane wave background perturbed by random noise only if baseband MI is present. Furthermore, the development of an individual RW will not be “masked” by the growth of the noise if the MI itself is not too strong. Even more illuminating information is revealed with disturbance of a specified wavelength (or a narrow range of frequency input). A disturbance with wave numbers in the passband will not generate any coherent structures, but those in the baseband may generate an Akhmediev breather or a RW‐like structure.

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Rogue waves of the Sasa-Satsuma equation in a chaotic wave field

Cited by 53 publications

References 41 publications

Rogue wave spectra of the Kundu-Eckhaus equation

Rogue wave spectra of the Kundu-Eckhaus equation

State transition induced by higher-order effects and background frequency

Rogue Waves for an Alternative System of Coupled Hirota Equations: Structural Robustness and Modulation Instabilities

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