On the existence of chirped algebraic solitary waves in optical fibers governed by Kundu–Eckhaus equation

Triki, Houria; Sun, Yunzhou; Biswas, Anjan; Zhou, Qin; Yıldırım, Yakup; Yu, Zhong; Alshehri, Hashim M.

doi:10.1016/j.rinp.2022.105272

Cited by 21 publications

(6 citation statements)

References 52 publications

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“…Most studies of chirped solitary waves have been limited to Kerr type media and in the paraxial regime often in presence of self-steepening and with Raman frequency shifting terms It is customary to assume that the phase factor responsible for giving rise to chirped solitary waves has a quadratic dependence on the pulse amplitude, i.e. it is proportional to the intensity [22][23][24][25]. However, as described in this article the chirp can also be inversely dependent on the intensity [26].…”

Section: Y B Y Y Y D Y Ny Y My Ymentioning

confidence: 99%

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On conservation laws, their applications in stability analysis and chirped solitary wave solutions for the generalized Schrödinger–Hirota equation and its reductions

Dan,

Garai,

Ghose-Choudhury

et al. 2024

Phys. Scr.

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Conserved quantities for a generalized version of the Schr"{o}dinger-Hirota (SH) equation and its reductions are deduced using an algorithmic approach which is easier to implement compared to more sophisticated mathematical methods. The conserved mass and the Hamiltonian, whenever it exists, are then used to analyse the stability of exact stationary wave solutions, by invoking the Vakhitov-Kolokolov criterion and variational methods. In addition we have focussed on two classes of chirped solitary wave solutions for reductions of the generalised SH equation, namely the algebraic and the hyperbolic classes. It is found that along with the regular dependance of the chirp on the intensity there may even be an additional dependence varying inversely on the intensity of the solitary wave. The chirped hyperbolic solutions are found to correspond to gray solitary waves for suitable parameter values which may also flip to anti-dark solitary waves depending on the ratio of the parameters involved in the solution.

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Section: Y B Y Y Y D Y Ny Y My Ymentioning

confidence: 99%

“…These solutions are usually taken in the form of rational functions. We consider two cases following [22].…”

Section: Algebraic Solitary Wavesmentioning

confidence: 99%

On conservation laws, their applications in stability analysis and chirped solitary wave solutions for the generalized Schrödinger–Hirota equation and its reductions

Dan,

Garai,

Ghose-Choudhury

et al. 2024

Phys. Scr.

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“…This limits the effect of the NLS solutions on the original carrier wave to simply a constant, time-independent frequency shift. To break this spectral symmetry, it is necessary to appeal to higher-order effects within the weakly nonlinear theory that induce self-frequency shifting as has been explored in optics (Palacios et al 1999;Goyal et al 2011;Triki et al 2016Triki et al , 2022.…”

Section: Spectral Asymmetry and The Emergence Of Chirpmentioning

confidence: 99%

The nonlinear evolution of whistler-mode chorus: modulation instability as the source of tones

Ratliff,

Allanson

2023

J. Plasma Phys.

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We review the modulation stability of parallel-propagating/field-aligned whistler-mode chorus (WMC) waves propagating in a warm plasma from a formal perspective with a focus on wave–particle interactions via ponderomotive forces. The modulation instability criteria are characterised by the group velocity dispersion,$d c_g/dk$, for whistler-mode waves and a condition on the ratio between the group velocity$c_g$and the electron sound speed$c_{s,e}$. We also demonstrate that in order to investigate the spatiotemporal evolution of the envelope and the formation of packets (according to this mechanism), one necessarily needs to account for the motion of ions within the system, leading to an ionic influence on the modulation instability threshold determined by the ion fraction of the plasma. Finally, we demonstrate that chirping may be captured when higher-order effects are included within the spatiotemporal evolution of the amplitude. This yields not only an explicit expression for the sweep rate but also identifies a possible origin for the power band gap that occurs at half the electron gyrofrequency. Numerical validation demonstrates that the interaction between wave packets is a source for the emergence of tones observed within mission data, and such interactions may be a major source of the electron energisation which WMC are responsible for.

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“…Many experts have dealt with various mathematical models to derive miscellaneous types of chirped solitons by means of several analytical techniques. Some of obtained soliton structures include kink, dark and bright solitons [36][37][38][39]; chirped self-similar bright and kink solitons [40]; dark-dark and bright-bright soliton pairs [41]; chirped self-similar gray and kink waves [42], see also [43][44][45][46]. Our present work focuses on deriving chirped optical soliton solutions in fiber BGs.…”

Section: Introductionmentioning

confidence: 99%

Chirped gap solitons in fiber Bragg gratings with polynomial law of nonlinear refractive index

Al-Ghafri¹,

Sankar²,

Krishnan

et al. 2023

J. Eur. Opt. Society-Rapid Publ.

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The objective of the present study is to examine the behaviors of chirped optical solitons in fiber Bragg gratings (BGs) with dispersive reflectivity. The form of nonlinear refractive index represents polynomial law nonlinearity. By virtue of phase-matching condition, the discussed model of coupled nonlinear Schrödinger equation is reduced to an integrable form. Consequently, chirped optical solitons having various profiles such as W-shaped, bright, dark, kink and anti-kink solitons are derived. Further to this, the chirp associated with these soliton structures are extracted. The impact of dispersive reflectivity, self-phase modulation and cross-phase modulation on the pulse propagation is investigated and it is induced that the changes of self-phase modulation and cross-phase modulation cause a marked rise in soliton amplitude which is subject to minor variations by dispersive reflectivity. The physical evolutions of chirped optical solitons are described along with the corresponding chirp to pave the way for possible applications in the field of fiber BGs.

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On the existence of chirped algebraic solitary waves in optical fibers governed by Kundu–Eckhaus equation

Cited by 21 publications

References 52 publications

On conservation laws, their applications in stability analysis and chirped solitary wave solutions for the generalized Schrödinger–Hirota equation and its reductions

On conservation laws, their applications in stability analysis and chirped solitary wave solutions for the generalized Schrödinger–Hirota equation and its reductions

The nonlinear evolution of whistler-mode chorus: modulation instability as the source of tones

Chirped gap solitons in fiber Bragg gratings with polynomial law of nonlinear refractive index

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