Persistence of rogue waves in extended nonlinear Schrödinger equations: Integrable Sasa–Satsuma case

Bandelow, U.; Akhmediev, Nail

doi:10.1016/j.physleta.2012.03.032

Cited by 112 publications

(92 citation statements)

References 19 publications

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“…1. This feature had been observed before [40] but was presented without any explanation. Interestingly, this tilt also appears in the orientation of the waves created in a chaotic wave field.…”

Section: Rogue-wave Solutionsmentioning

confidence: 76%

“…The exact rogue-wave solution of the SSE has been presented for the first time in the work [40]. The solution is cumbersome and will not be reproduced here.…”

Section: Rogue-wave Solutionsmentioning

confidence: 99%

“…The expression given in Ref. [41] is simply translated along the τ and x axes in comparison to the original result [40]. The solution given in Fig.…”

Section: Rogue-wave Solutionsmentioning

confidence: 99%

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

et al. 2014

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We study the properties of the chaotic wave fields generated in the frame of the Sasa-Satsuma equation (SSE). Modulation instability results in a chaotic pattern of small-scale filaments with a free parameter-the propagation constant k. The average velocity of the filaments is approximately given by the group velocity calculated from the dispersion relation for the plane-wave solution. Remarkably, our results reveal the reason for the skewed profile of the exact SSE rogue-wave solutions, which was one of their distinctive unexplained features. We have also calculated the probability density functions for various values of the propagation constant k, showing that probability of appearance of rogue waves depends on k.

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Section: Rogue-wave Solutionsmentioning

confidence: 76%

“…The exact rogue-wave solution of the SSE has been presented for the first time in the work [40]. The solution is cumbersome and will not be reproduced here.…”

Section: Rogue-wave Solutionsmentioning

confidence: 99%

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

et al. 2014

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“…Since then, optical rogue waves have been observed in several systems [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25], and their study has advanced the research in the field, in a way that has been compared to the introduction of optical systems to study chaos in the 1980s [26].…”

mentioning

confidence: 99%

Rogue waves in optically injected lasers: Origin, predictability, and suppression

et al. 2013

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Rogue waves are devastating extreme events that occur in many natural systems, and a lot of work has focused on predicting and understanding their origin. In optically injected semiconductor lasers rogue waves are rare ultra-high pulses that sporadically occur in the laser chaotic output intensity. Here we show that these optical rogue waves can be predicted with long anticipation time, that they are generated by a crisis-like process, and that noise can be employed to either enhance or suppress their probability of occurrence. By providing a good understanding of the mechanisms triggering and controlling the rogue waves, our results can contribute to improve the performance of injected lasers and can also enable new experiments to test if these mechanisms are also involved in other natural systems where rogue waves have been observed. Extreme events are often catastrophic ones, such as tsunamis, earthquakes, supernovas, stock market crashes, etc. [1][2][3][4][5]. Ocean rogue waves, also referred to as freak waves, are several times the average height of surrounding waves and have steep, fast rising, and fast falling sides, like "a wall of water" [6][7][8][9]. They are a topic of intensive research as they can develop suddenly even in calm and apparently safe seas and have been responsible for several boat accidents, representing a major challenge for the design of off-shore platforms for the oil and gas industry.In optics, Solli et al.[10] have shown that extremely broadband radiation can be generated from a narrow-band input, with a long-tailed distribution similar to that of ocean rogue waves. Since then, optical rogue waves have been observed in several systems [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25], and their study has advanced the research in the field, in a way that has been compared to the introduction of optical systems to study chaos in the 1980s [26].In lasers, rogue waves occurring in the form of giant intensity pulses capable of producing catastrophic optical damage have been observed in pump-modulated [19], Raman [20], mode-locked [21][22][23], and optically injected lasers [24]. In Ref.[24] the rogue waves were studied in the framework of a simple and deterministic model that exhibits two types of chaos: one in which rogue waves do not appear consistently and one in which they are relatively frequent [24]. Since a deterministic chaotic system possesses some correlation length, the rogue waves in the system should have some degree of predictability.Here we show, experimentally and numerically, that these optical rogue waves can indeed be predicted with a long anticipation time as compared with the laser characteristic time scales. In addition, we show that an external crisis-like process [27,28], in the form of the crossing of the attractor, developed from one fixed point, with the stable manifold of another fixed point, gives rise to an expanded attractor that supports trajectories with rogue waves. We also show that noise can be exploited for either enhancing or suppressing ...

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“…Rogue wave is a kind of waves that seems abnormal which is first observed in the deep ocean. Recently, rogue wave solutions in other more complex systems have been sought by using the Darboux dressing technique or Hirota bilinear method [3,13,15,16,22,30,31]. Periodic breather, Akhmediev breather, Ma breather and rogue wave solutions are obtained for the coupled long-wave-short-wave system by using a Hirota two-soliton method with complex frequency and complex wave number [23].…”

Section: Introductionmentioning

confidence: 99%

New homoclinic rogue wave solution for the coupled Schrodinger- Boussinesq equation

Longxing¹,

Dai²

2017

J. Nonlinear Sci. Appl.

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Exact homoclinic breather wave solution for the coupled Schrödinger-Boussinesq equation is obtained by using homoclinic test technique. Based on the homoclinic breather wave solution, rational homoclinic breather wave solution is generated by homoclinic breather limit method, rogue wave in the form of the rational homoclinic solution is derived when the period of homoclinic breather wave goes to infinite. This is a new way for generating rogue wave which is different from direct constructing method, Darboux dressing technique and ansätz with complexity of parameter. This result shows the homoclinic rogue wave can be generated from homoclinic breather wave, and it is useful for explaining some related nonlinear phenomenon.

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Persistence of rogue waves in extended nonlinear Schrödinger equations: Integrable Sasa–Satsuma case

Cited by 112 publications

References 19 publications

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

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

Rogue waves in optically injected lasers: Origin, predictability, and suppression

New homoclinic rogue wave solution for the coupled Schrodinger- Boussinesq equation

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