Complementary optical rogue waves in parametric three-wave mixing

Chen, Shihua; Cai, Xian-Ming; Grelu, Philippe; Soto-Crespo, J. M.; Wabnitz, Stefan; Baronio, Fabio

doi:10.1364/oe.24.005886

Cited by 25 publications

(24 citation statements)

References 40 publications

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“…suggesting that the matter-wave components are endowed with a complementary rogue wave property similar to that obtained for the degenerate TWRI system [39]. Let us pay more attention on these solutions, which basically hold true for arbitrary b values.…”

Section: Integrable Nls-mb Model and Exact Rogue Wave Solutionsmentioning

confidence: 55%

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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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Section: Integrable Nls-mb Model and Exact Rogue Wave Solutionsmentioning

confidence: 55%

“…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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Section: Akhmediev Breather Classification In a Two-component Casementioning

confidence: 99%

“…For fixed parameters a i , b i (i = 1, 2), one can determine the spectral point λ for which there are two roots with the same image part of (14). To achieve this aim, we firstly solve the equation (14). In general, the quantic equation can be solved with formula (14), but it is rather so complex that we can not analyze it conveniently.…”

Section: Akhmediev Breather Classification In a Two-component Casementioning

confidence: 99%

“…RWs are found to have many different fundamental patterns, such as eye-shaped one, anti-eye-shaped one, and four-petaled one, etc. Scalar ones usually admit eye-shaped one [6,7], while vector ones admit anti-eye-shaped one and four-petaled one [8,9,10,11,12,13,14]. ABs with infinite period tend to be RW, but ABs with finite period admit different pattern with RW (the hump amplification rate is different and the valley values are also distinctive).…”

Section: Introductionmentioning

confidence: 99%

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Modulational instability and homoclinic orbit solutions in vector nonlinear Schrödinger equation

Ling

Zhao

2019

Communications in Nonlinear Science and Numerical Simulation

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Modulational instability has been used to explain the formation of breather and rogue waves qualitatively. In this paper, we show modulational instability can be used to explain the structure of them in a quantitative way. We develop a method to derive general forms for Akhmediev breather and rogue wave solutions in a N -component nonlinear Schrödinger equations. The existence condition for each pattern is clarified clearly. Moreover, the general multi-high-order rogue wave solutions and multi-Akhmediev breather solutions for N -component nonlinear Schrödinger equations are constructed. The results further deepen our understanding on the quantitative relations between modulational instability and homoclinic orbits solutions.

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Breather‐to‐soliton transitions and nonlinear wave interactions for the nonlinear Schrödinger equation with the sextic operators in optical fibers

Sun

2016

Annalen der Physik

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We find that the sextic nonlinear Schrödinger (NLS) equation admits breather-to-soliton transitions. With the Darboux transformation, analytic breather solutions with imaginary eigenvalues up to the second order are explicitly presented. The condition for breather-to-soliton transitions is explicitly presented and several examples of transitions are shown. Interestingly, we show that the sextic NLS equation admits not only the breather-to-bright-soliton transitions but also the breather-to-dark-soliton transitions. We also show the interactions between two solitons on the constant backgrounds, as well as between breather and soliton.

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Complementary optical rogue waves in parametric three-wave mixing

Cited by 25 publications

References 40 publications

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

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

Modulational instability and homoclinic orbit solutions in vector nonlinear Schrödinger equation

Breather‐to‐soliton transitions and nonlinear wave interactions for the nonlinear Schrödinger equation with the sextic operators in optical fibers

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