Velocity-Locked Solitary Waves in Quadratic Media

Baronio, Fabio; Conforti, Matteo; Angelis, C. De; Degasperis, A.; Andreana, Marco; Couderc, Vincent; Barthélémy, Alain

doi:10.1103/physrevlett.104.113902

Cited by 37 publications

(30 citation statements)

References 17 publications

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“…Otherwise, when there is passband MI we only observed the generation of nonlinear wave oscillations. Based on the above findings, we are led to believe that the conditions for simultaneous rogue-wave existence and of baseband MI may also be extended to other relevant, integrable, and nonintegrable physical models of great interest for applications, for instance, consider frequency conversion models [34,35] where extreme wave events and complex breaking behaviors are known to take place [36,37].…”

Section: Discussionmentioning

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: Discussionmentioning

confidence: 99%

Baseband modulation instability as the origin of rogue waves

et al. 2015

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“…Hereafter we consider the 3WRI equations (2) with (η 1 , η 2 , η 3 ) = (+, −, +), namely only the soliton exchange type interaction since this is the case relevant to recently found results [25][26][27][29][30][31][32][33][34]. With no loss of generality, we shall use coordinates (x, t) such that V 3 = 0.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…The focus in the present paper is on the spectral theory of the three-wave interaction equation with the purpose of numerically integrating the spectral equation for both vanishing and non vanishing boundary values. In particular we apply spectral techniques to recently found theoretical and experimental results on the three-wave resonant interaction processes [25][26][27][28][29][30][31][32][33][34].…”

Section: Introductionmentioning

confidence: 99%

The Three-Wave Resonant Interaction Equations: Spectral and Numerical Methods

et al. 2010

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Abstract. The spectral theory of the integrable partial differential equations which model the resonant interaction of three waves is considered with the purpose of numerically solving the direct spectral problem for both vanishing and non vanishing boundary values. Methods of computing both the continuum spectrum data and the discrete spectrum eigenvalues are given together with examples of such computations. The explicit spectral representation of the Manley-Rowe invariants is also displayed. Mathematics Subject Classification (2000). 74J30, 37K15, 65Z05.

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“…(1) are also termed the SIT-NLS equations [40]. They constitute a peculiar vector system, since only the electric field truly propagates along the z direction, whereas the matter-wave evolutions are each expressed by a first-order derivative with respect to t. This is a fundamental difference between this vector system and those composed of coupled optical waves, such as the TWRI system mentioned earlier [35,36].…”

Section: Theoretical Frameworkmentioning

confidence: 99%

“…For the latter case, three field components are involved, which respect momentum and energy conservation during interaction. They admit as well coherent localized structures such as solitons [35,36] and rogue waves [37][38][39].…”

Section: Introductionmentioning

confidence: 99%

Optical Peregrine rogue waves of self-induced transparency in a resonant erbium-doped fiber

Chen

Baronio

et al. 2017

Opt. Express

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Abstract:The resonant interaction of an optical field with two-level doping ions in a cryogenic optical fiber is investigated within the framework of nonlinear Schrödinger and Maxwell-Bloch equations. We present explicit fundamental rational rogue wave solutions in the context of self-induced transparency for the coupled optical and matter waves. It is exhibited that the optical wave component always features a typical Peregrine-like structure, while the matter waves involve more complicated yet spatiotemporally balanced amplitude distribution. The existence and stability of these rogue waves is then confirmed by numerical simulations, and they are shown to be excited amid the onset of modulation instability. These solutions can also be extended, using the same analytical framework, to include higher-order dispersive and nonlinear effects, highlighting their universality.

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Velocity-Locked Solitary Waves in Quadratic Media

Cited by 37 publications

References 17 publications

Baseband modulation instability as the origin of rogue waves

Baseband modulation instability as the origin of rogue waves

The Three-Wave Resonant Interaction Equations: Spectral and Numerical Methods

Optical Peregrine rogue waves of self-induced transparency in a resonant erbium-doped fiber

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