Linear instability of the Peregrine breather: Numerical and analytical investigations

Calini, Annalisa; Schober, C. M.; Strawn, M.

doi:10.1016/j.apnum.2018.11.005

Cited by 22 publications

(5 citation statements)

References 25 publications

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“…As for more complex and fundamental higher-order NLSE solutions on a condensate, in its core there is still an integrable NLSE. Therefore, NLSE-based techniques can be inherently useful for analysis of the solutions, such as a higher-order Akhmediev-, Kusnetsov-Ma, and Peregrine-type solutions [36][37][38][39][40], which will be our work in future. Therefore, NFT provide an alternative way to describe solitons in general, which compliments temporal and spectral measurement.…”

Section: Resultsmentioning

confidence: 99%

Nonlinear Fourier transform assisted high-order soliton characterization

Wang

Chen

et al. 2022

New J. Phys.

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Nonlinear Fourier transform (NFT), based on the nonlinear Schrödinger equation (NLSE), is implemented for the description of soliton propagation, and in particular focused on propagation of high-order solitons. In nonlinear frequency domain, a high-order soliton has multiple eigenvalues depending on the soliton amplitude and pulse-width. During the propagation along the standard single mode fiber (SSMF), their eigenvalues remain constant, while the corresponding discrete spectrum rotates along with the SSMF transmission. Consequently, we can distinguish the soliton order based on its eigenvalues. Meanwhile, the discrete spectrum rotation period is consistent with the temporal evolution period of the high-order solitons. The discrete spectrum contains nearly 99.99% energy of a soliton pulse. After inverse-NFT (INFT) on discrete spectrum, soliton pulse can be reconstructed, illustrating that the eigenvalues can be used to characterize soliton pulse with good accuracy. This work shows that soliton characteristics can be well described in the nonlinear frequency domain. Moreover, as a significant supplement to the existing means of characterizing soliton pulses, NFT is expected to be another fundamental optical processing method besides an oscilloscope (measuring pulse time domain information) and a spectrometer (measuring pulse frequency domain information).

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Section: Resultsmentioning

confidence: 99%

Nonlinear Fourier transform assisted high-order soliton characterization

Wang

Chen

et al. 2022

New J. Phys.

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“…On the other hand, Voronovich et al confirmed numerically that the bottom friction effect, even when it is small in comparison to the nonlinear term, could hamper the formation of a breather freak wave at the nonlinear stage of instability [134]. Investigations on linear stability demonstrated that the Peregrine soliton is unstable against all standard perturbations, where the analytical study is supported by numerical evidence [135][136][137][138].…”

Section: The Peregrine Solitonmentioning

confidence: 94%

Peregrine Soliton as a Limiting Behavior of the Kuznetsov-Ma and Akhmediev Breathers

Karjanto

2021

Front. Phys.

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This article discusses a limiting behavior of breather solutions of the focusing nonlinear Schrödinger equation. These breathers belong to the family of solitons on a non-vanishing and constant background, where the continuous-wave envelope serves as a pedestal. The rational Peregrine soliton acts as a limiting behavior of the other two breather solitons, i.e., the Kuznetsov-Ma breather and Akhmediev soliton. Albeit with a phase shift, the latter becomes a nonlinear extension of the homoclinic orbit waveform corresponding to an unstable mode in the modulational instability phenomenon. All breathers are prototypes for rogue waves in nonlinear and dispersive media. We present a rigorous proof using the ϵ-δ argument and show the corresponding visualization for this limiting behavior.

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“…Investigations on linear stability demonstrated that the Peregrine soliton is unstable against all standard perturbations, where the analytical study is supported by numerical evidence. [145][146][147][148].…”

Section: The Peregrine Solitonmentioning

confidence: 99%

Peregrine soliton as a limiting behavior of the Kuznetsov-Ma and Akhmediev breathers

Karjanto¹

2020

Preprint

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This article discusses a limiting behavior of breather solutions of the focusing nonlinear Schr ödinger (NLS) equation. These breathers belong to the families of solitons on a nonvanishing and constant background, where the continuous-wave envelope serves as a pedestal. The rational Peregrine soliton acts as a limiting behavior of the other two breather solitons, i.e., the Kuznetsov-Ma breather and Akhmediev soliton. Albeit with a phase shift, the latter becomes a nonlinear extension of the homoclinic orbit waveform corresponding to an unstable mode in the modulational instability phenomenon. All breathers are prototypes for rogue waves in nonlinear and dispersive media. We present a rigorous proof using the ǫ-δ argument and show the corresponding visualization for this limiting behavior.

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Linear instability of the Peregrine breather: Numerical and analytical investigations

Cited by 22 publications

References 25 publications

Nonlinear Fourier transform assisted high-order soliton characterization

Nonlinear Fourier transform assisted high-order soliton characterization

Peregrine Soliton as a Limiting Behavior of the Kuznetsov-Ma and Akhmediev Breathers

Peregrine soliton as a limiting behavior of the Kuznetsov-Ma and Akhmediev breathers

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