Financial Rogue Waves

Yan, Zhenya

doi:10.1088/0253-6102/54/5/31

Cited by 377 publications

(194 citation statements)

References 19 publications

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“…The rogue waves were first observed in ocean [30], now it can be seen in plasmas, atmospheric physics, optics, stock market crashes [31], and super-fluid helium [32].…”

Section: Here the Normalization Constant Ismentioning

confidence: 99%

Heavy ion-acoustic rogue waves in electron-positron multi-ion plasmas

Chowdhury

Mannan

Hasan

et al. 2017

Chaos: An Interdisciplinary Journal of Nonlinear Science

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The nonlinear propagation of heavy-ion-acoustic (HIA) waves (HIAWs) in a four component multi-ion plasma (containing inertial heavy negative ions and light positive ions, as well as inertialess nonextensive electrons and positrons) has been theoretically investigated. The nonlinear Schrödinger (NLS) equation is derived by employing the reductive perturbation method. It is found that the NLS equation leads to the modulational instability (MI) of HIAWs, and to the formation of HIA rogue waves (HIARWs), which are due to the effects of nonlinearity and dispersion in the propagation of HIAWs. The conditions for MI of HIAWs, and the basic properties of the generated HIARWs are identified. It is observed that the striking features (viz. instability criteria, growth rate of MI, amplitude and width of HIARWs, etc.) of the HIAWs are significantly modified by effects of nonextensivity of electrons and positrons, ratio of light positive ion mass to heavy negative ion mass, ratio of electron number density to light positive ion number density, and ratio of electron temperature to positron temperature, etc. The relevancy of our present investigation to the observations in the space (viz. cometary comae and earth's ionosphere) and laboratory (laser plasma interaction experimental devices) plasmas is pointed out. I. LEAD PARAGRAPHA new electron-positron, multi-ion plasma model has been considered to identify new features (instability criteria, growth rate of MI, amplitude and width, etc.) of heavy ion-acoustic rogue waves. This rogue waves are associated with nonlinear propagation of HIAWs in which the inertia (restoring force) is mainly provided by the heavy negative ions (nonextensive electron and positron temperatures) and are appeared as the solutions of NLS equation (derived here by the reductive perturbation method) in unstable parametric regime. The new striking features of these HIARWs are identified and are found to be applicable in the space and laboratories plasmas. II. INTRODUCTIONOver the last few decades, wave dynamics in electronpositron-ion (e-p-i) plasmas is one of the major research area for the plasma physicists because of painstaking experimental observational evidence in both space (viz. [15]. Similarly positrons can be generated in modern laser plasma experiments when ultra-intense laser pulse interacts with matter [16,17].In case of space and laboratory plasmas, all time particles do not follow Maxwellian distribution (which is a velocity distribution describing the plasma particles in a thermal equilibrium [18][19][20]). Although, a large number of authors considered that plasma components are in thermal equilibrium but due to the some external disturbances (e.g. wave-particle interactions, external force fields present in natural space plasma environments, and turbulence, etc.) their assumption is no longer valid. In space and astrophysical environments, the Maxwellian distribution is no longer exist when the plasma particles move very fast compared to their thermal velocities. Non-extensive generaliza...

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“…The rogue waves were first observed in ocean [30], now it can be seen in plasmas, atmospheric physics, optics, stock market crashes [31], and super-fluid helium [32].…”

Section: Here the Normalization Constant Ismentioning

confidence: 99%

Heavy ion-acoustic rogue waves in electron-positron multi-ion plasmas

Chowdhury

Mannan

Hasan

et al. 2017

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…The RWs have also been observed experimentally in physical systems such as water wave tank [22], capillary waves [23] and nonlinear optics [5,24]. Several theoretical studies on the dynamics of RWs in nonlinear fiber optics [25,26], plasma physics [27], laser-plasma interactions [28], and even econophysics [29], described by scalar NLS equation, have been made in recent times. Now, as mentioned in the beginning, the dynamics of a cigar shaped BEC at absolute zero temperature is usually described by the mean-field GP equation (1), which is a generalized form of the ubiquitous constant coefficient NLS equation (2), for the wave function of the condensate.…”

Section: Introductionmentioning

confidence: 99%

Manipulating matter rogue waves and breathers in Bose-Einstein condensates

et al. 2014

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We construct higher order rogue wave solutions and breather profiles for the quasi-one-dimensional Gross-Pitaevskii equation with a time-dependent interatomic interaction and external trap through the similarity transformation technique. We consider three different forms of traps, namely (i) timeindependent expulsive trap, (ii) time-dependent monotonous trap and (iii) time-dependent periodic trap. Our results show that when we change a parameter appearing in the time-independent or time-dependent trap the second and third-order rogue waves transform into the first-order like rogue waves. We also analyze the density profiles of breather solutions. Here also we show that the shapes of the breathers change when we tune the strength of trap parameter. Our results may help to manage rogue waves experimentally in a BEC system.

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“…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].…”

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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Financial Rogue Waves

Cited by 377 publications

References 19 publications

Heavy ion-acoustic rogue waves in electron-positron multi-ion plasmas

Heavy ion-acoustic rogue waves in electron-positron multi-ion plasmas

Manipulating matter rogue waves and breathers in Bose-Einstein condensates

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

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