Modulation instability gain and discrete soliton interaction in gyrotropic molecular chain

Abbagari, Souleymanou; Houwe, Alphonse; Akinyemi, Lanre; Saliou, Youssoufa; Bouetou, Thomas B.

doi:10.1016/j.chaos.2022.112255

Cited by 66 publications

(18 citation statements)

References 21 publications

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“…Many works have been carried out on discrete MI growth rates [12,[16][17][18]. Diverse parameters are used to highlight the dynamical instabilities, from where an exponential grows of the plane-wave amplitude is obtained.…”

Section: Modulation Instability Growth Ratementioning

confidence: 99%

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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Section: Modulation Instability Growth Ratementioning

confidence: 99%

Nonlinear localized wave modes in optomechanical array

Houwe,

Djorwé,

Souleymanou

et al. 2023

Phys. Scr.

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“…However, when more complex effects exist in a model, the MI analysis and the exact solution of the model become more complicated, which is one of the reasons for the emergence of multiband MI. For example, higher-order MI in the coupled system leads to breather and RW with multi-petal [32,33]; cross-phase modulation or four-wave mixing effects can cause MI to produce sidebands [34,35]; semi-discrete models have periodic unstable bands [36][37][38], etc. In particular, recent studies have shown that the higher-order dispersion in continuous systems can make modulation stable (MS) regions occurring in the MI region, which leads to the state transition of the localized wave [13].…”

Section: Introductionmentioning

confidence: 99%

Modulation instability and localized wave excitations for a higher-order modified self-steepening nonlinear Schrödinger equation in nonlinear optics

Wang,

Zhou,

Yang

et al. 2023

Proc. R. Soc. A.

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This paper investigates a higher-order modified nonlinear Schrödinger equation with higher-order dispersion and self-steepening effects, which can be used to study the dynamics of asymmetric and steepened optical pulse transmission in optical fibres. The modulation instability of the plane-wave solution has been analysed, and the state transition of the rogue waves under the higher-order dispersion effect is presented. The findings demonstrate that the self-steepening effect may also produce an asymmetric unstable frequency band. Combined with the modulation instability, the rogue wave, rational soliton and mixed interaction of localized waves have a quantitative relationship with plane-wave parameters. Various exact solutions can be accurately located and obtained according to the generalized Darboux transformation. The asymptotic analysis of rational solutions demonstrates the state transition of higher-order rogue waves. This paper illustrates the significance of modulation instability for studying the integrable systems by the Darboux transformation. It is a new guidance to solve the difficulty of exact excitation of asymmetric localized waves in complex integrable systems. The results have prospective applications and references for the emergence, amplification and compression of asymmetric pulses in optical experiments.

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“…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). In [26], the NLSE has been established to drive one end of the discrete molecular chain and soliton interactions were depicted. So, it is obvious today that the DNLSE and other nonlinear equations are widely used in several nonlinear systems.…”

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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Modulation instability gain and discrete soliton interaction in gyrotropic molecular chain

Cited by 66 publications

References 21 publications

Nonlinear localized wave modes in optomechanical array

Nonlinear localized wave modes in optomechanical array

Modulation instability and localized wave excitations for a higher-order modified self-steepening nonlinear Schrödinger equation in nonlinear optics

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

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