Modulational instability in nonlinear saturable media with competing nonlocal nonlinearity

Tabi, Conrad Bertrand; Tagwo, Hippolyte; Kofané, Timoléon Crépin

doi:10.1103/physreve.106.054201

Cited by 24 publications

(7 citation statements)

References 99 publications

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“…and Γ th the TA and Ω the driven external frequency. Inserting equation (8) into equation (5), at the upper frequency band the TA expression is given by:…”

Section: Nonlinear Generation Modesmentioning

confidence: 99%

“…Investigation of nonlinear wave in the structures where nonlinearity and dispersion terms are competing has growing this last decade. Many mathematical model have been derived to carry out this matter [1][2][3][4][5][6][7]. In Cavity Optomechanics (COM), some relevant works have been pointed out concerning solitonic waves [8,9].…”

Section: Introductionmentioning

confidence: 99%

“…In nonlinear structure, where nonlinear and dispersion terms interact, MI is crucial for the process of generating the localized wave patterns such as dark soliton, bright soliton, rogue wave and breather [2,4,12]. MI has been carried out in several structures such as nonlinear optics [5], and fluid dynamics [6]. In our previous work, we have shown that for small perturbations, the variation of the self-Kerr nonlinear term expands the MI growth rates and the MI bands are widely increased [12].…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear localized wave modes in optomechanical array

Houwe,

Djorwé,

Souleymanou

et al. 2023

Phys. Scr.

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Optomechanical arrays have been used in many areas of research, from nonlinear optics to acoustics. In particular, the optomechanical array has been studied for its interesting properties such as strong optical force and high frequency resonance. In this work, we carry out the modulated wave patterns and nonlinear modes by driving one end of the optomechanical array in the forbidden gap. We use the discrete nonlinear Schr"{o}dinger equation with self-Kerr nonlinear term to determine the threshold amplitude. We then consider the driven amplitude to drive the model above the phonon band. The result is a train of waves with an asymmetric shape in the forbidden gap. For large values of the nonlinear term, we observe unstable modes of the modulation growth rates and the modulated wave patterns also emerge from the driven optomechanical array. At the specific cell index, the pulse train increases in amplitude and brings instability in the bandgap. These results open a new feature of the position modulated self-Kerr nonlinear term as an internal force to drive the nonlinear Schr"{o}dinger equation.

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“…and Γ th the TA and Ω the driven external frequency. Inserting equation (8) into equation (5), at the upper frequency band the TA expression is given by:…”

Section: Nonlinear Generation Modesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Nonlinear localized wave modes in optomechanical array

Houwe,

Djorwé,

Souleymanou

et al. 2023

Phys. Scr.

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“…In [11], the authors have depicted the chaos-like motion and unstable modes incited by the self-modulated Kerr nonlinearity in optomechanical arrays. The discrete nonlinear Schrödinger equation (DNLSE) is the most well-known discrete model during MI analysis, and localized modes [1][2][3][4][5][6][7][8][9][10][11]. For example, in [25] the authors used the discrete cubic-quintic NLSE to show the effects of the nonlinear terms on the train of waves propagating in the forbidden gap (FG).…”

Section: Introductionmentioning

confidence: 99%

Discrete modulation instability and localized waves of the coupled semi-discrete Hirota equation

Houwe

Abbagari

Akinyemi

et al. 2023

Preprint

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In this paper, we use the numerical simulation of the discrete Hirota equation to point out the localized modes and wave patterns. The discrete modulation instability is used to demonstrate how the nonlinear term generates unstable or stable modes when a little perturbation is introduced. We have also stated that for strong enough nonlinear terms, new bands emerge. Furthermore, by applying an external periodic force, we were able to push one end of the discrete Hirota model into the forbidden frequency gap. We established the threshold amplitude expression and the driven amplitude. According to one finding, the threshold of supratransmission decreases as the nonlinear term of the discrete Hirota equation increases. For specific times of propagation, we showed the propagation of the train of waves as well as the modulated wave patterns. We demonstrated the wave train traveling through the band gap, where energy jumps from the bottom to the top and vice versa, over a significant period of time. These findings will almost certainly pave the way for new nonlinear dynamics applications.

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“…Since then, many studies have been conducted to investigate MI's properties in nonlinear media with a nonlocal response. For example, a linear perturbation analysis of MI in the one-dimensional (1D) system was conducted considering a general nonlinear response function [25,26]. In doing so, different response functions were used to compute MI gain profiles.…”

Section: Introductionmentioning

confidence: 99%

Nonlocal cubic and quintic nonlinear wave patterns in pure-quartic media

Tiofack

Tabi

Tagwo

et al. 2023

J. Opt.

Self Cite

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In this work, pure-quartic soliton formation is investigated in the framework of a nonlinear Schrödinger equation with competing Kerr (cubic) and non-Kerr (quintic) nonlocal nonlinearities and quartic dispersion. In the process, the modulational instability (MI) phenomenon is activated under a suitable balance between the nonlocal nonlinearities and the quartic dispersion, both for exponential and rectangular nonlocal nonlinear responses. Interestingly, the maximum MI growth rate and bandwidth are reduced or can completely be suppressed for some specific values of the cubic and quintic nonlocality parameters, depending on the type of nonlocal response. The analytical results are confirmed via direct numerical simulations, where the instability supports the signature of pure-quartic dark and bright solitons. These results may provide a better understanding of pure-quartic solitonic structures for their potential applications in the next generation of nonlinear optical devices.

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Modulational instability in nonlinear saturable media with competing nonlocal nonlinearity

Cited by 24 publications

References 99 publications

Nonlinear localized wave modes in optomechanical array

Nonlinear localized wave modes in optomechanical array

Discrete modulation instability and localized waves of the coupled semi-discrete Hirota equation

Nonlocal cubic and quintic nonlinear wave patterns in pure-quartic media

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