Статті в журналах: "Peregrine Soliton"

1

Van Gorder, Robert A. "Orbital Instability of the Peregrine Soliton." Journal of the Physical Society of Japan 83, no. 5 (May 15, 2014): 054005. http://dx.doi.org/10.7566/jpsj.83.054005.

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2

Kibler, B., K. Hammani, J. Fatome, G. Millot, C. Finot, G. Genty, M. Erkintalo, et al. "The Peregrine Soliton Observed At Last." Optics and Photonics News 22, no. 12 (December 1, 2011): 30. http://dx.doi.org/10.1364/opn.22.12.000030.

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3

Kibler, B., J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley. "The Peregrine soliton in nonlinear fibre optics." Nature Physics 6, no. 10 (August 22, 2010): 790–95. http://dx.doi.org/10.1038/nphys1740.

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4

Al Khawaja, U., H. Bahlouli, M. Asad-uz-zaman, and S. M. Al-Marzoug. "Modulational instability analysis of the Peregrine soliton." Communications in Nonlinear Science and Numerical Simulation 19, no. 8 (August 2014): 2706–14. http://dx.doi.org/10.1016/j.cnsns.2014.01.002.

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5

Hennig, Dirk, Nikos I. Karachalios, and Jesús Cuevas-Maraver. "The closeness of localized structures between the Ablowitz–Ladik lattice and discrete nonlinear Schrödinger equations: Generalized AL and DNLS systems." Journal of Mathematical Physics 63, no. 4 (April 1, 2022): 042701. http://dx.doi.org/10.1063/5.0072391.

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Анотація:

The Ablowitz–Ladik system, being one of the few integrable nonlinear lattices, admits a wide class of analytical solutions, ranging from exact spatially localized solitons to rational solutions in the form of the spatiotemporally localized discrete Peregrine soliton. Proving a closeness result between the solutions of the Ablowitz–Ladik system and a wide class of Discrete Nonlinear Schrödinger systems in a sense of a continuous dependence on their initial data, we establish that such small amplitude waveforms may be supported in nonintegrable lattices for significantly large times. Nonintegrable systems exhibiting such behavior include a generalization of the Ablowitz–Ladik system with power-law nonlinearity and the discrete nonlinear Schrödinger equation with power-law and saturable nonlinearities. The outcome of numerical simulations illustrates, in excellent agreement with the analytical results, the persistence of small amplitude Ablowitz–Ladik analytical solutions in all the nonintegrable systems considered in this work, with the most striking example being that of the Peregine soliton.

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6

Chen, Shihua, and Lian-Yan Song. "Peregrine solitons and algebraic soliton pairs in Kerr media considering space–time correction." Physics Letters A 378, no. 18-19 (March 2014): 1228–32. http://dx.doi.org/10.1016/j.physleta.2014.02.042.

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7

Yurova, Alla. "A hidden life of Peregrine's soliton: Rouge waves in the oceanic depths." International Journal of Geometric Methods in Modern Physics 11, no. 06 (July 2014): 1450057. http://dx.doi.org/10.1142/s0219887814500571.

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Although the Peregrine-type solutions of the nonlinear Schrödinger (NLS) equation have long been associated mainly with the infamous "rouge waves" on the surface of the ocean, they might have a much more interesting role in the oceanic depths; in this paper we show that these solutions play an important role in the evolution of the intrathermocline eddies, also known as the "oceanic lenses". In particular, we show that the collapse of a lens is determined by the particular generalization of the Peregrine soliton — the so-called exultons — of the NLS equation. In addition, we introduce a new mathematical method of construction of a vortical filament (a frontal zone of a lens) from a known one by the Darboux transformation.

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8

Hammani, Kamal, Bertrand Kibler, Christophe Finot, Philippe Morin, Julien Fatome, John M. Dudley, and Guy Millot. "Peregrine soliton generation and breakup in standard telecommunications fiber." Optics Letters 36, no. 2 (January 5, 2011): 112. http://dx.doi.org/10.1364/ol.36.000112.

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9

Guo, Lehui, Ping Chen, and Jinshou Tian. "Peregrine combs and rogue waves on a bright soliton background." Optik 227 (February 2021): 165455. http://dx.doi.org/10.1016/j.ijleo.2020.165455.

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10

Hussain, Akhtar, Hassan Ali, M. Usman, F. D. Zaman, and Choonkil Park. "Some New Families of Exact Solitary Wave Solutions for Pseudo-Parabolic Type Nonlinear Models." Journal of Mathematics 2024 (March 31, 2024): 1–19. http://dx.doi.org/10.1155/2024/5762147.

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Анотація:

The objective of the current study is to provide a variety of families of soliton solutions to pseudo-parabolic equations that arise in nonsteady flows, hydrostatics, and seepage of fluid through fissured material. We investigate a class of such equations, including the one-dimensional Oskolkov (1D OSK), the Benjamin-Bona-Mahony (BBM), and the Benjamin-Bona-Mahony-Peregrine-Burgers (BBMPB) equation. The Exp (-ϕξ)-expansion method is used for new hyperbolic, trigonometric, rational, exponential, and polynomial function-based solutions. These solutions of the pseudo-parabolic class of partial differential equations (PDEs) studied here are new and novel and have not been reported in the literature. These solutions depict the hydrodynamics of various soliton shapes that can be utilized to study the nature of traveling wave solutions of other nonlinear PDE’s.

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11

Essama, Bedel Giscard Onana, Salome Ndjakomo Essiane, Frederic Biya-Motto, Bibiane Mireille Ndi Nnanga, Mohammed Shabat, and Jacques Atangana. "Peregrine Soliton and Akhmediev Breathers in a Chameleon Electrical Transmission Line." Journal of Applied Mathematics and Physics 08, no. 12 (2020): 2775–92. http://dx.doi.org/10.4236/jamp.2020.812205.

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12

Zhang, Yu-Ping, Lan Yu, and Guang-Mei Wei. "Integrable aspects and rogue wave solution of Sasa–Satsuma equation with variable coefficients in the inhomogeneous fiber." Modern Physics Letters B 32, no. 05 (February 20, 2018): 1850059. http://dx.doi.org/10.1142/s0217984918500598.

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Анотація:

Under investigation with symbolic computation in this paper, is a variable-coefficient Sasa–Satsuma equation (SSE) which can describe the ultra short pulses in optical fiber communications and propagation of deep ocean waves. By virtue of the extended Ablowitz–Kaup–Newell–Segur system, Lax pair for the model is directly constructed. Based on the obtained Lax pair, an auto-Bäcklund transformation is provided, then the explicit one-soliton solution is obtained. Meanwhile, an infinite number of conservation laws in explicit recursion forms are derived to indicate its integrability in the Liouville sense. Furthermore, exact explicit rogue wave (RW) solution is presented by use of a Darboux transformation. In addition to the double-peak structure and an analog of the Peregrine soliton, the RW can exhibit graphically an intriguing twisted rogue-wave (TRW) pair that involve four well-defined zero-amplitude points.

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13

Chabchoub, A., S. Neumann, N. P. Hoffmann, and N. Akhmediev. "Spectral properties of the Peregrine soliton observed in a water wave tank." Journal of Geophysical Research: Oceans 117, no. C11 (February 7, 2012): n/a. http://dx.doi.org/10.1029/2011jc007671.

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14

Su, Qingtang. "Partial Justification of the Peregrine Soliton from the 2D Full Water Waves." Archive for Rational Mechanics and Analysis 237, no. 3 (May 12, 2020): 1517–613. http://dx.doi.org/10.1007/s00205-020-01535-1.

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15

Shrira, Victor I., and Vladimir V. Geogjaev. "What makes the Peregrine soliton so special as a prototype of freak waves?" Journal of Engineering Mathematics 67, no. 1-2 (October 20, 2009): 11–22. http://dx.doi.org/10.1007/s10665-009-9347-2.

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16

Albalawi, Wedad, Rabia Jahangir, Waqas Masood, Sadah A. Alkhateeb, and Samir A. El-Tantawy. "Electron-Acoustic (Un)Modulated Structures in a Plasma Having (r, q)-Distributed Electrons: Solitons, Super Rogue Waves, and Breathers." Symmetry 13, no. 11 (October 27, 2021): 2029. http://dx.doi.org/10.3390/sym13112029.

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Анотація:

The propagation of electron-acoustic waves (EAWs) in an unmagnetized plasma, comprising (r,q)-distributed hot electrons, cold inertial electrons, and stationary positive ions, is investigated. Both the unmodulated and modulated EAWs, such as solitary waves, rogue waves (RWs), and breathers are discussed. The Sagdeev potential approach is employed to determine the existence domain of electron acoustic solitary structures and study the perfectly symmetric planar nonlinear unmodulated structures. Moreover, the nonlinear Schrödinger equation (NLSE) is derived and its modulated solutions, including first order RWs (Peregrine soliton), higher-order RWs (super RWs), and breathers (Akhmediev breathers and Kuznetsov–Ma soliton) are presented. The effects of plasma parameters and, in particular, the effects of spectral indices r and q, of distribution functions on the characteristics of both unmodulated and modulated EAWs, are examined in detail. In a limited cases, the (r,q) distribution is compared with Maxwellian and kappa distributions. The present investigation may be beneficial to comprehend and predict the modulated and unmodulated electron acoustic structures in laboratory and space plasmas.

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17

Dai, Chao-Qing, and Yue-Yue Wang. "Controllable combined Peregrine soliton and Kuznetsov–Ma soliton in $${\varvec{\mathcal {PT}}}$$ PT -symmetric nonlinear couplers with gain and loss." Nonlinear Dynamics 80, no. 1-2 (January 10, 2015): 715–21. http://dx.doi.org/10.1007/s11071-015-1900-0.

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18

Chaachoua Sameut, H., Sakthivinayagam Pattu, U. Al Khawaja, M. Benarous, and H. Belkroukra. "Peregrine Soliton Management of Breathers in Two Coupled Gross–Pitaevskii Equations with External Potential." Physics of Wave Phenomena 28, no. 3 (July 2020): 305–12. http://dx.doi.org/10.3103/s1541308x20030036.

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19

Liu, Wei. "High-order rogue waves of the Benjamin–Ono equation and the nonlocal nonlinear Schrödinger equation." Modern Physics Letters B 31, no. 29 (October 17, 2017): 1750269. http://dx.doi.org/10.1142/s0217984917502694.

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Анотація:

High-order rogue wave solutions of the Benjamin–Ono equation and the nonlocal nonlinear Schrödinger equation are derived by employing the bilinear method, which are expressed by simple polynomials. Typical dynamics of these high-order rogue waves are studied by analytical and graphical ways. For the Benjamin–Ono equation, there are two types of rogue waves, namely, bright rogue waves and dark rogue waves. In particular, the fundamental rogue wave pattern is different from the usual fundamental rogue wave patterns in other soliton equations. For the nonlocal nonlinear Schrödinger equation, the exact explicit rogue wave solutions up to the second order are presented. Typical rogue wave patterns such as Peregrine-type, triple and fundamental rogue waves are put forward. These high-order rogue wave patterns have not been shown before in the nonlocal Schrödinger equation.

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20

Sharma, S. K., and H. Bailung. "Observation of hole Peregrine soliton in a multicomponent plasma with critical density of negative ions." Journal of Geophysical Research: Space Physics 118, no. 2 (February 2013): 919–24. http://dx.doi.org/10.1002/jgra.50111.

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21

Cuevas-Maraver, J., Boris A. Malomed, P. G. Kevrekidis, and D. J. Frantzeskakis. "Stabilization of the Peregrine soliton and Kuznetsov–Ma breathers by means of nonlinearity and dispersion management." Physics Letters A 382, no. 14 (April 2018): 968–72. http://dx.doi.org/10.1016/j.physleta.2018.02.013.

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22

Li, Ji-tao, Jin-zhong Han, Yuan-dong Du, and Chao-Qing Dai. "Controllable behaviors of Peregrine soliton with two peaks in a birefringent fiber with higher-order effects." Nonlinear Dynamics 82, no. 3 (July 7, 2015): 1393–98. http://dx.doi.org/10.1007/s11071-015-2246-3.

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23

Zhang, Jie-Fang, Ding-Guo Yu, and Mei-Zhen Jin. "Self-similar transformation and excitation of rogue waves for (2+1)-dimensional Zakharov equation." Acta Physica Sinica 71, no. 8 (2022): 084204. http://dx.doi.org/10.7498/aps.71.20211181.

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Анотація:

The search for the excitation of two-dimensional rogue wave in a (2+1)-dimensional nonlinear evolution model is a research hotspot. In this paper, the self-similar transformation of the (2+1)-dimensional Zakharov equation is established, and this equation is transformed into the (1+1)-dimensional nonlinear Schrödinger equation. Based on the similarity transformation and the rational formal solution of the (1+1)-dimensional nonlinear Schrödinger equation, the rogue wave excitation of the (2+1)-dimensional Zakharov equation is obtained by selecting appropriate parameters. We can see that the shape and amplitude of the rogue waves can be effectively controlled. Finally, the propagation characteristics of line rogue waves are diagrammed visually. We also find that the line-type characteristics of two-dimensional rogue wave are present in the x-y plane when the parameter <inline-formula><tex-math id="M5">\begin{document}$ \gamma = 1 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="8-20211181_M5.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="8-20211181_M5.png"/></alternatives></inline-formula>. The line rogue wave is converted into discrete localized rogue wave in the x-y plane when the parameter <inline-formula><tex-math id="M6">\begin{document}$ \gamma \ne 1 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="8-20211181_M6.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="8-20211181_M6.png"/></alternatives></inline-formula>. The spatial localized rogue waves with short-life can be obtained in the required x-y plane region. This is similar to the Peregrine soliton (PS) first discovered by Peregrine in the (1+1)-dimensional NLS equation, which is the limit case of the “Kuznetsov-Ma soliton” (KMS) or “Akhmediev breather” (AB). The proposed approach to constructing the line rogue waves of the (2+1) dimensional Zakharov equation can serve as a potential physical mechanism to excite two-dimensional rogue waves, and can be extended to other (2+1)-dimensional nonlinear systems.

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24

Maleewong, Montri, and Roger H. J. Grimshaw. "Evolution of Water Wave Groups in the Forced Benney–Roskes System." Fluids 8, no. 2 (February 2, 2023): 52. http://dx.doi.org/10.3390/fluids8020052.

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For weakly nonlinear waves in one space dimension, the nonlinear Schrödinger Equation is widely accepted as a canonical model for the evolution of wave groups described by modulation instability and its soliton and breather solutions. When there is forcing such as that due to wind blowing over the water surface, this can be supplemented with a linear growth term representing linear instability leading to the forced nonlinear Schrödinger Equation. For water waves in two horizontal space dimensions, this is replaced by a forced Benney–Roskes system. This is a two-dimensional nonlinear Schrödinger Equation with a nonlocal nonlinear term. In deep water, this becomes a local nonlinear term, and it reduces to a two-dimensional nonlinear Schrödinger Equation. In this paper, we numerically explore the evolution of wave groups in the forced Benney–Roskes system using four cases of initial conditions. In the one-dimensional unforced nonlinear Schrödinger equa tion, the first case would lead to a Peregrine breather and the second case to a line soliton; the third case is a long-wave perturbation, and the fourth case is designed to stimulate modulation instability. In deep water and for finite depth, when there is modulation instability in the one-dimensional nonlinear Schdrödinger Equation, the two-dimensional simulations show a similar pattern. However, in shallow water where there is no one-dimensional modulation instability, the extra horizontal dimension is significant in producing wave growth through modulation instability.

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25

Zhang, Xing, Yin-Chuan Zhao, Feng-Hua Qi, and Liu-Ying Cai. "Characteristics of nonautonomous W-shaped soliton and Peregrine comb in a variable-coefficient higher-order nonlinear Schrödinger equation." Superlattices and Microstructures 100 (December 2016): 934–40. http://dx.doi.org/10.1016/j.spmi.2016.10.072.

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26

Li, Ji-tao, Xian-tu Zhang, Ming Meng, Quan-tao Liu, Yue-yue Wang, and Chao-qing Dai. "Control and management of the combined Peregrine soliton and Akhmediev breathers in $${\mathcal {PT}}$$ PT -symmetric coupled waveguides." Nonlinear Dynamics 84, no. 2 (November 19, 2015): 473–79. http://dx.doi.org/10.1007/s11071-015-2500-8.

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27

Zhou, Haoqi, Shuwei Xu, and Maohua Li. "Peregrine Rogue Waves Generated by the Interaction and Degeneration of Soliton-Like Solutions: Derivative Nonlinear Schrödinger Equation." Journal of Applied Mathematics and Physics 08, no. 12 (2020): 2824–35. http://dx.doi.org/10.4236/jamp.2020.812208.

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28

Baronio, Fabio, Shihua Chen, and Stefano Trillo. "Resonant radiation from Peregrine solitons." Optics Letters 45, no. 2 (January 10, 2020): 427. http://dx.doi.org/10.1364/ol.381228.

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29

Wu, Zhen-Kun, Yun-Zhe Zhang, Yi Hu, Feng Wen, Yi-Qi Zhang, and Yan-Peng Zhang. "The Interaction of Peregrine Solitons." Chinese Physics Letters 31, no. 9 (September 2014): 090502. http://dx.doi.org/10.1088/0256-307x/31/9/090502.

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30

Hu, X., J. Guo, Y. F. Song, L. M. Zhao, L. Li, and D. Y. Tang. "Dissipative peregrine solitons in fiber lasers." Journal of Physics: Photonics 2, no. 3 (July 7, 2020): 034011. http://dx.doi.org/10.1088/2515-7647/ab95f3.

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31

Lu, Dianchen, Aly R. Seadawy, and Iftikhar Ahmed. "Peregrine-like rational solitons and their interaction with kink wave for the resonance nonlinear Schrödinger equation with Kerr law of nonlinearity." Modern Physics Letters B 33, no. 24 (August 30, 2019): 1950292. http://dx.doi.org/10.1142/s0217984919502920.

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Анотація:

By utilizing the logarithmic transformation and symbolic computation with ansatz functions technique, Peregrine-like rational solitons are obtained for the resonance nonlinear Schrödinger equation (R-NLSE) with Kerr law of nonlinearity. Meanwhile, the interaction between rational solitons and the kink wave is also investigated. The dynamics and many important properties of these obtained solutions are analyzed and briefly described in figures by selecting the appropriate parametric values.

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32

Wu Da, 武达, 王娟芬 Wang Juanfen, 石佳 Shi Jia, 张朝霞 Zhang Zhaoxia, and 杨玲珍 Yang Lingzhen. "Generation and Transmission of Peregrine Solitons in Doped Fiber." Acta Optica Sinica 37, no. 4 (2017): 0406002. http://dx.doi.org/10.3788/aos201737.0406002.

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33

Wazwaz, Abdul-Majid, and Lakhveer Kaur. "Optical solitons and Peregrine solitons for nonlinear Schrödinger equation by variational iteration method." Optik 179 (February 2019): 804–9. http://dx.doi.org/10.1016/j.ijleo.2018.11.004.

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34

Zhang, Jie-Fang, Ding-Guo Yu, and Mei-Zhen Jin. "Two-dimensional self-similarity transformation theory and line rogue waves excitation." Acta Physica Sinica 71, no. 1 (2022): 014205. http://dx.doi.org/10.7498/aps.71.20211417.

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Анотація:

A two-dimensional self-similarity transformation theory is established, and the focusing (parabolic) (2 + 1)-dimensional NLS equation is taken as the model. The two-dimensional self-similarity transformation is proposed for converting the focusing (2 + 1)-dimensional NLS equation into the focusing (1 + 1) dimensional NLS equations, and the excitation of its novel line-rogue waves is further investigated. It is found that the spatial coherent structures induced by the Akhmediev breathers (AB) and Kuznetsov-Ma solitons (KMS) also have the short-lived characteristics which are possessed by the line-rogue waves induced by the Peregrine solitons, and the other higher-order rogue waves and the multi-rogue waves of the (1 + 1) dimensional NLS equations. This is completely different from the evolution characteristics of spatially coherent structures induced by bright solitons (including multi-solitons and lump solutions), with their shapes and amplitudes kept unchanged. The diagram shows the evolution characteristics of all kinds of resulting line rogue waves. The new excitation mechanism of line rogue waves revealed contributes to the new understanding of the coherent structure of high-dimensional nonlinear wave models.

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35

Hoffmann, C., E. G. Charalampidis, D. J. Frantzeskakis, and P. G. Kevrekidis. "Peregrine solitons and gradient catastrophes in discrete nonlinear Schrödinger systems." Physics Letters A 382, no. 42-43 (October 2018): 3064–70. http://dx.doi.org/10.1016/j.physleta.2018.08.014.

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36

Ye, Yanlin, Yi Zhou, Shihua Chen, Fabio Baronio, and Philippe Grelu. "General rogue wave solutions of the coupled Fokas–Lenells equations and non-recursive Darboux transformation." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 475, no. 2224 (April 2019): 20180806. http://dx.doi.org/10.1098/rspa.2018.0806.

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Анотація:

We formulate a non-recursive Darboux transformation technique to obtain the general n th-order rational rogue wave solutions to the coupled Fokas–Lenells system, which is an integrable extension of the noted Manakov system, by considering both the double-root and triple-root situations of the spectral characteristic equation. Based on the explicit fundamental and second-order rogue wave solutions, we demonstrate several interesting rogue wave dynamics, among which are coexisting rogue waves and anomalous Peregrine solitons. Our solutions are generalized to include the complete background-field parameters and therefore helpful for future experimental study.

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37

Guan, J., C. J. Zhu, C. Hang, and Y. P. Yang. "Generation and propagation of hyperbolic secant solitons, Peregrine solitons, and breathers in a coherently prepared atomic system." Optics Express 28, no. 21 (October 5, 2020): 31287. http://dx.doi.org/10.1364/oe.398424.

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38

González-Gaxiola, O., and Anjan Biswas. "Akhmediev breathers, Peregrine solitons and Kuznetsov-Ma solitons in optical fibers and PCF by Laplace-Adomian decomposition method." Optik 172 (November 2018): 930–39. http://dx.doi.org/10.1016/j.ijleo.2018.07.102.

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39

Pathak, Pallabi, Sumita K. Sharma, Y. Nakamura, and H. Bailung. "Observation of ion acoustic multi-Peregrine solitons in multicomponent plasma with negative ions." Physics Letters A 381, no. 48 (December 2017): 4011–18. http://dx.doi.org/10.1016/j.physleta.2017.10.046.

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40

DUAN Ya-juan, 段亚娟, and 宋丽军 SONG Li-jun. "Influence of the Self-Steepening and Raman Gain Effects on the Chirped Peregrine Solitons." Acta Sinica Quantum Optica 23, no. 3 (2017): 270–75. http://dx.doi.org/10.3788/jqo20172303.0009.

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41

Mahato, Dipti Kanika, A. Govindarajan, M. Lakshmanan, and Amarendra K. Sarma. "Dispersion managed generation of Peregrine solitons and Kuznetsov-Ma breather in an optical fiber." Physics Letters A 392 (March 2021): 127134. http://dx.doi.org/10.1016/j.physleta.2020.127134.

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42

Uthayakumar, T., L. Al Sakkaf, and U. Al Khawaja. "Peregrine Solitons of the Higher-Order, Inhomogeneous, Coupled, Discrete, and Nonlocal Nonlinear Schrödinger Equations." Frontiers in Physics 8 (December 3, 2020). http://dx.doi.org/10.3389/fphy.2020.596886.

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Анотація:

This study reviews the Peregrine solitons appearing under the framework of a class of nonlinear Schrödinger equations describing the diverse nonlinear systems. The historical perspectives include the various analytical techniques developed for constructing the Peregrine soliton solutions, followed by the derivation of the general breather solution of the fundamental nonlinear Schrödinger equation through Darboux transformation. Subsequently, we collect all forms of nonlinear Schrödinger equations, involving systematically the effects of higher-order nonlinearity, inhomogeneity, external potentials, coupling, discontinuity, nonlocality, higher dimensionality, and nonlinear saturation in which Peregrine soliton solutions have been reported.

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43

Caso-Huerta, M., L. Bu, S. Chen, S. Trillo, and F. Baronio. "Peregrine solitons and resonant radiation in cubic and quadratic media." Chaos: An Interdisciplinary Journal of Nonlinear Science 34, no. 7 (July 1, 2024). http://dx.doi.org/10.1063/5.0216445.

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We present the fascinating phenomena of resonant radiation emitted by transient rogue waves in cubic and quadratic nonlinear media, particularly those shed from Peregrine solitons, one of the main wavepackets used today to model real-world rogue waves. In cubic media, it turns out that the emission of radiation from a Peregrine soliton can be attributed to the presence of higher-order dispersion, but is affected by the intrinsic local longitudinal variation of the soliton wavenumber. In quadratic media, we reveal that a two-color Peregrine rogue wave can resonantly radiate dispersive waves even in the absence of higher-order dispersion, subjected to a phase-matching mechanism that involves the second-harmonic wave, and to a concomitant difference-frequency generation process. In both cubic and quadratic media, we provide simple analytic criteria for calculating the radiated frequencies in terms of material parameters, showing excellent agreement with numerical simulations.

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44

Coulibaly, Saliya, Camus G. L. Tiofack, and Marcel G. Clerc. "Spatiotemporal Complexity Mediated by Higher-Order Peregrine-Like Extreme Events." Frontiers in Physics 9 (March 22, 2021). http://dx.doi.org/10.3389/fphy.2021.644584.

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The Peregrine soliton is the famous coherent solution of the non-linear Schrödinger equation, which presents many of the characteristics of rogue waves. Usually studied in conservative systems, when dissipative effects of injection and loss of energy are included, these intrigued waves can disappear. If they are preserved, their role in the dynamics is unknown. Here, we consider this solution in the framework of dissipative systems. Using the paradigmatic model of the driven and damped non-linear Schrödinger equation, the profile of a stationary Peregrine-type solution has been found. Hence, the Peregrine soliton waves are persistent in systems outside of the equilibrium. In the weak dissipative limit, analytical description has a good agreement with the numerical simulations. The stability has been studied numerically. The large bursts that emerge from the instability are analyzed by means of the local largest Lyapunov exponent. The observed spatiotemporal complexity is ruled by the unstable second-order Peregrine-type soliton.

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45

Wang, Xiu-Bin. "Exotic dynamics of breather and rogue waves in a coupled nonlinear Schrödinger equation." Modern Physics Letters B, October 30, 2023. http://dx.doi.org/10.1142/s0217984924500829.

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Under investigation in this work is a coupled nonlinear Schrödinger equation (CNLSE), which can be used to describe the dynamics of light beams and pulses in [Formula: see text]-symmetric coupled waveguides. Its breather wave (BW) and rogue wave (RW) solutions are presented here. The BW solutions can be converted into various soliton solutions including the Akhmediev breather, Kuznetsov–Ma soliton breather and Peregrine soliton. The dynamics of the solutions are graphically discussed. Moreover, we observe that the two BWs can evolve into an Akhmediev breather with a Peregrine soliton. We hope that the results can be used to enrich dynamical behavior of BWs and rogue waves in the CNLSE.

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46

Karjanto, Natanael. "Peregrine Soliton as a Limiting Behavior of the Kuznetsov-Ma and Akhmediev Breathers." Frontiers in Physics 9 (September 27, 2021). http://dx.doi.org/10.3389/fphy.2021.599767.

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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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47

Tikan, Alexey, Stéphane Randoux, Gennady El, Alexander Tovbis, Francois Copie, and Pierre Suret. "Local Emergence of Peregrine Solitons: Experiments and Theory." Frontiers in Physics 8 (February 5, 2021). http://dx.doi.org/10.3389/fphy.2020.599435.

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It has been shown analytically that Peregrine solitons emerge locally from a universal mechanism in the so-called semiclassical limit of the one-dimensional focusing nonlinear Schrödinger equation. Experimentally, this limit corresponds to the strongly nonlinear regime where the dispersion is much weaker than nonlinearity at initial time. We review here evidences of this phenomenon obtained on different experimental platforms. In particular, the spontaneous emergence of coherent structures exhibiting locally the Peregrine soliton behavior has been demonstrated in optical fiber experiments involving either single pulse or partially coherent waves. We also review theoretical and numerical results showing the link between this phenomenon and the emergence of heavy-tailed statistics (rogue waves).

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48

Chabchoub, Amin, Alexey Slunyaev, Norbert Hoffmann, Frederic Dias, Bertrand Kibler, Goëry Genty, John M. Dudley, and Nail Akhmediev. "The Peregrine Breather on the Zero-Background Limit as the Two-Soliton Degenerate Solution: An Experimental Study." Frontiers in Physics 9 (August 25, 2021). http://dx.doi.org/10.3389/fphy.2021.633549.

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Solitons are coherent structures that describe the nonlinear evolution of wave localizations in hydrodynamics, optics, plasma and Bose-Einstein condensates. While the Peregrine breather is known to amplify a single localized perturbation of a carrier wave of finite amplitude by a factor of three, there is a counterpart solution on zero background known as the degenerate two-soliton which also leads to high amplitude maxima. In this study, we report several observations of such multi-soliton with doubly-localized peaks in a water wave flume. The data collected in this experiment confirm the distinctive attainment of wave amplification by a factor of two in good agreement with the dynamics of the nonlinear Schrödinger equation solution. Advanced numerical simulations solving the problem of nonlinear free water surface boundary conditions of an ideal fluid quantify the physical limitations of the degenerate two-soliton in hydrodynamics.

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49

Pathak, Pallabi. "Ion Acoustic Peregrine Soliton Under Enhanced Dissipation." Frontiers in Physics 8 (February 19, 2021). http://dx.doi.org/10.3389/fphy.2020.603112.

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The effect of enhanced Landau damping on the evolution of ion acoustic Peregrine soliton in multicomponent plasma with negative ions has been investigated. The experiment is performed in a multidipole double plasma device. To enhance the ion Landau damping, the temperature of the ions is increased by applying a continuous sinusoidal signal of frequency close to the ion plasma frequency ∼1 MHz to the separation grid. The spatial damping rate of the ion acoustic wave is measured by interferometry. The damping rate of ion acoustic wave increases with the increase in voltage of the applied signal. At a higher damping rate, the Peregrine soliton ceases to show its characteristics leaving behind a continuous envelope.

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50

Chen, Shihua, Yanlin Ye, Jose M. Soto-Crespo, Philippe Grelu, and Fabio Baronio. "Peregrine Solitons Beyond the Threefold Limit and Their Two-Soliton Interactions." Physical Review Letters 121, no. 10 (September 6, 2018). http://dx.doi.org/10.1103/physrevlett.121.104101.

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