Rogue waves in coupled Hirota systems

Chen, Shihua; Song, Lian-Yan

doi:10.1103/physreve.87.032910

Cited by 139 publications

(91 citation statements)

References 44 publications

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“…When compared to scalar dynamical systems, vector systems may allow for energy transfer between their different degrees of freedom, which potentially yields rich and significant new families of vector rogue-wave solutions. Rogue-wave families have been recently found as solutions of the vector NLSE (VNLSE) [15][16][17][18], the three-wave resonant interaction equations [19], the coupled Hirota equations [20], and the long-wave-short-wave (LWSW) resonance [21].…”

Section: Introductionmentioning

confidence: 99%

Baseband modulation instability as the origin of rogue waves

et al. 2015

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We study the existence and properties of rogue-wave solutions in different nonlinear wave evolution models that are commonly used in optics and hydrodynamics. In particular, we consider the Fokas-Lenells equation, the defocusing vector nonlinear Schrödinger equation, and the long-wave-short-wave resonance equation. We show that rogue-wave solutions in all of these models exist in the subset of parameters where modulation instability is present if and only if the unstable sideband spectrum also contains cw or zero-frequency perturbations as a limiting case (baseband instability). We numerically confirm that rogue waves may only be excited from a weakly perturbed cw whenever the baseband instability is present. Conversely, modulation instability leads to nonlinear periodic oscillations.

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Section: Introductionmentioning

confidence: 99%

Baseband modulation instability as the origin of rogue waves

et al. 2015

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“…Firstly, there are some new excitation patterns for vector RW, in contrast to the well-known eye-shaped one in scalar system [1][2][3][4]. For example, dark RW was presented numerically [5] and analytically [6][7][8] for two-component coupled systems. Four-petaled RW was reported recently in three-component coupled systems [9,10], and even two-component coupled system [11].…”

Section: Introductionmentioning

confidence: 99%

High-order rogue wave solutions for the coupled nonlinear Schrödinger equations-II

Zhao

Guo

Ling

2016

Journal of Mathematical Physics

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We study on dynamics of high-order rogue wave in two-component coupled nonlinear Schrödinger equations. Based on the generalized Darboux transformation and formal series method, we obtain the high-order rogue wave solution without the special limitation on the wave vectors. As an application, we exhibit the first, second-order rogue wave solution and the superposition of them by computer plotting. We find the distribution patterns for vector rogue waves are much more abundant than the ones for scalar rogue waves, and also different from the ones obtained with the constrain conditions on background fields. The results further enrich and deep our realization on rogue wave excitation dynamics in such diverse fields as Bose-Einstein condensates, nonlinear fibers, and superfluids.

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“…When compared to scalar dynamical systems, vector systems generally allow energy transfer between their additional degrees of freedom, which potentially yields families of intricate vector rogue-wave solutions. Indeed, rogue-wave families with complicated rational forms have been recently found in the Davey-Stewartson equation [23], the coupled Manakov system [24], and the coupled Hirota equations [25]. Let us recall that the scalar NLS equation does not admit single dark-rogue-wave solutions, even in the case of a defocusing nonlinearity.…”

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confidence: 99%

Dark- and bright-rogue-wave solutions for media with long-wave–short-wave resonance

2014

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Exact explicit rogue-wave solutions of intricate structures are presented for the long-wave-short-wave resonance equation. These vector parametric solutions feature coupled dark-and bright-field counterparts of the Peregrine soliton. Numerical simulations show the robustness of dark and bright rogue waves in spite of the onset of modulational instability. Dark fields originate from the complex interplay between anomalous dispersion and the nonlinearity driven by the coupled long wave. This unusual mechanism, not available in scalar nonlinear wave equation models, can provide a route to the experimental realization of dark rogue waves in, for instance, negative index media or with capillary-gravity waves. Because of their dramatic and potentially devastating manifestations, oceanic rogue waves have been the focus of intense research for more than a decade [1,2]. The roguewave terminology itself refers to the adverse surprise that is experienced when a transient giant wave of extreme amplitude or steepness is suddenly formed in the vicinity of a cruising ship [3]. In addition to being deployed into the safer and controllable environment of water tanks [4,5], rogue-wave research is also spreading widely to other disciplines that share general features of nonlinearity and complexity. These new avenues for rogue-wave research include fluid dynamics [6][7][8], nonlinear optics and lasers [9][10][11][12], plasma physics [13], and Bose-Einstein condensation [14]. The possibility to accede to a general understanding of rogue-wave formation is still an open question [15]. Nonetheless, the debate stimulates the comparison of predictions and observations between distinct areas, such as hydrodynamics and nonlinear optics, in situations where analogous dynamics can be identified through a common equation model. So far, the nonlinear Schrödinger (NLS) equation has played such a pivotal role.The Peregrine soliton, predicted 30 years ago [16], is the simplest rogue-wave solution associated with the NLS equation and it has recently been observed experimentally in a water-wave tank [4], a multicomponent plasma [13], and an optical fiber [10]. It is of fundamental significance because it is robust [17] and serves as the prototypical rogue-wave profile in various experimental fields. Indeed, the Peregrine soliton, as opposed to ordinary solitons that can be traced over long propagation distances, is localized in both transverse and propagation dimensions, thus reflecting the seemingly unpredictable appearance of a rogue wave [4,18]. Mathematically, the Peregrine soliton and related rogue-wave solutions of higher-order [5] While rogue-wave investigation is flourishing in several fields of science, there is a necessity to go beyond the standard NLS description in order to model important classes of physical systems in a relevant way. One recent development consists in including dissipative terms since a substantial supply of energy-from the wind in oceanography to the pump for laser cavities [19]-is generally required to drive roguew...

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Rogue waves in coupled Hirota systems

Cited by 139 publications

References 44 publications

Baseband modulation instability as the origin of rogue waves

Baseband modulation instability as the origin of rogue waves

High-order rogue wave solutions for the coupled nonlinear Schrödinger equations-II

Dark- and bright-rogue-wave solutions for media with long-wave–short-wave resonance

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