Rogue Waves Emerging from the Resonant Interaction of Three Waves

Baronio, Fabio; Conforti, Matteo; Degasperis, A.; Lombardo, Sara

doi:10.1103/physrevlett.111.114101

Cited by 211 publications

(134 citation statements)

References 40 publications

(70 reference statements)

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“…For example, it has been shown that RW attracts dark-bright wave. In threecomponent coupled system, four-petaled flower structure RW was reported very recently in [29,30]. These studies indicate that there are much abundant pattern dynamics for RW in the multi-component coupled systems, which are quite distinctive from the ones in scalar systems.…”

mentioning

confidence: 77%

High-order rogue waves in vector nonlinear Schrödinger equations

Ling

Guo

Zhao³

2014

Phys. Rev. E

162

122

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We study on dynamics of high-order rogue wave in two-component coupled nonlinear Schrödinger equations. We find four fundamental rogue waves can emerge for second-order vector RW in the coupled system, in contrast to the high-order ones in single component systems. The distribution shape can be quadrilateral, triangle, and line structures through varying the proper initial excitations given by the exact analytical solutions. Moreover, six fundamental rogue wave can emerge on the distribution for second-order vector rogue wave, which is similar to the scalar third-order ones. The distribution patten for vector ones are much abundant than the ones for scalar rogue waves. The results could be of interest in such diverse fields as Bose-Einstein condensates, nonlinear fibers, and superfluids. Introduction-Rogue wave (RW) is the name given by oceanographers to isolated large amplitude wave, which occurs more frequently then expected for normal, Gaussian distributed, statistical events [1][2][3]. It depicts a unique event that seems to appear from nowhere and disappear without a trace, and can appear in a variety of different contexts [4][5][6][7]. RW has been observed experimentally in nonlinear optics by Solli group and Kibler group [8,9], water wave tank by Chabchoub group [10], and even in plasma system by Bailung group [11]. These experimental studies suggest that the rational solutions of related dynamics equations can be used to describe these RW phenomena [12,13]. Moreover, there are many different pattern structures for high-order RW [14][15][16], which can be understood as a nonlinear superposition of fundamental RW (the first order RW). Recently, many efforts are devoted to classify the hierarchy for each order RW [17,18], since these superpositions are nontrivial and admit only a fixed number of elementary RWs in each high order solution (3 or 6 fundamental ones for the second order or third order one).

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mentioning

confidence: 77%

High-order rogue waves in vector nonlinear Schrödinger equations

Ling

Guo

Zhao³

2014

Phys. Rev. E

162

122

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“…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]. Secondly, the number of RW in temporal-spatial distribution plane is also different from the ones in scalar systems.…”

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 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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Rogue Waves Emerging from the Resonant Interaction of Three Waves

Cited by 211 publications

References 40 publications

High-order rogue waves in vector nonlinear Schrödinger equations

High-order rogue waves in vector nonlinear Schrödinger equations

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

Baseband modulation instability as the origin of rogue waves

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