Higher-order-effects management of soliton interactions in the Hirota equation

In ultrafast optics, optical pulses are generated to be of shorter pulse duration, which has enormous significance to industrial applications and scientific research. The ultrashort pulse evolution in fiber lasers can be described by the higher-order Ginzburg-Landau (GL) equation. However, analytic soliton solutions for this equation have not been obtained by use of existing methods. In this paper, a novel method is proposed to deal with this equation. The analytic soliton solution is obtained for the first time, and is proved to be stable against amplitude perturbations. Through the split-step Fourier method, the bright soliton solution is studied numerically. The analytic results here may extend the integrable methods, and could be used to study soliton dynamics for some equations in other disciplines. It may also provide the other way to obtain two-soliton solutions for higher-order GL equations.

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“…Besides, some ordinary phenomena, e.g. phase shift, amplification and compression, can be realized by modulating the related parameters 21 .…”

Section: Resultsmentioning

confidence: 99%

Novel asymmetric representation method for solving the higher-order Ginzburg-Landau equation

Wong

Pang

et al. 2016

Sci Rep

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“…This phenomenon caused a revolution in modern telecommunications process because when a light ray incident upon an optical fiber, it will split into two rays or a lot, which have slightly various paths under the polarization property. Recently, some studies have been established to discuss this phenomenon theoretically and experimentally via distinct published articles 2–22 through which the scientists have been shored that when the dispersion effect and nonlinear effect of the medium reach a stable equilibrium, the pulse can maintain its shape and velocity in the form of solitons during the transmission process 23–25 . The optical fiber transmission system is the ideal effective carrier one, which possesses high rate, large channel capacity, and no limitation of transmission distance, hence ensuring the high‐quality to long‐distance communications.…”

Section: Introductionmentioning

confidence: 99%

Unexpected configurations for the optical solitons propagation in lossy fiber system with dispersion terms effect

Zahran

Bekir

2022

Math Methods in App Sciences

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In this work, we will design unexpected configurations for the optical soliton propagation in lossy fiber system in the presence of the dispersion term solitons via two distinct and impressive techniques. The first one is the (G 0 /G)expansion method, while the second is solitary wave ansatze method. The two methods are implemented in the same vein and parallel. The obtained perceptions are new and were not achieved before. The comparison between our achieved visions and that achieved by other authors who used different schemas has been documented.the (G 0 /G)-expansion method, the lossy fiber system under dispersion terms influence, the optical soliton solutions, the solitary wave ansatze method

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“…In this paper, we consider a variable-coefficient NLS (vc-NLS) equation with higher-order effects as follows [35][36][37] …”

Section: Introductionmentioning

confidence: 99%

“…Liu et al have studied the two-soliton interactions of Eq. ( 1) analytically and numerically, and discussed the higherorder-effects management of soliton interactions [36]. He et al have investigated the control and manipulation of the rogue waves of Eq.…”

Section: Introductionmentioning

confidence: 99%

Breather transition dynamics, Peregrine combs and walls, and modulation instability in a variable-coefficient nonlinear Schrödinger equation with higher-order effects

et al. 2016

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We study a variable-coefficient nonlinear Schrödinger (vc-NLS) equation with higherorder effects. We show that the breather solution can be converted into four types of nonlinear waves on constant backgrounds including the multi-peak solitons, antidark soliton, periodic wave and W-shaped soliton. The transition condition requiring the group velocity dispersion (GVD) and third-order dispersion (TOD) to scale linearly is obtained analytically. We display several kinds of elastic interactions between the transformed nonlinear waves. We discuss the dispersion management of multi-peak soliton, which indicates that the GVD coefficient controls the number of peaks of the wave while the TOD coefficient has compression effect. The gain or loss has influence on the amplitudes of the multi-peak soliton. We further derive the breather multiple births by using multiple compression points of Akhmediev breathers in optical fiber systems with periodic dispersion. The number of ABs depends on the amplitude of the modulation but not on its wavelength, which affects their separation distance. In the limiting case, the breather multiple births reduce to the Peregrine combs. We discuss the effects of TOD coefficient on the spatiotemporal characteristics of Peregrine combs. When the amplitude of the modulation is equal to 1, the Peregrine comb is converted into a Peregrine wall that can be seen as intermediate state between rogue wave and W-shaped soliton. We finally find that the modulational stability regions with zero growth rate coincide with the transition condition using rogue wave eigenvalues. Our results could be useful for the experimental control and manipulation of the formation of generalized Peregrine rogue waves in diverse physical systems modeled by vc-NLS equation with higher-order effects.

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Higher-order-effects management of soliton interactions in the Hirota equation

Cited by 35 publications

References 53 publications

Novel asymmetric representation method for solving the higher-order Ginzburg-Landau equation

Novel asymmetric representation method for solving the higher-order Ginzburg-Landau equation

Unexpected configurations for the optical solitons propagation in lossy fiber system with dispersion terms effect

Breather transition dynamics, Peregrine combs and walls, and modulation instability in a variable-coefficient nonlinear Schrödinger equation with higher-order effects

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