Solitary wave solutions and modulational instability analysis of the nonlinear Schrödinger equation with higher-order nonlinear terms in the left-handed nonlinear transmission lines

Abdoulkary, Saïdou; Aboubakar, Amina; Aboubakar, Mahamoudou; Mohamadou, Alidou; Kavitha, L.

doi:10.1016/j.cnsns.2014.08.039

Cited by 24 publications

(12 citation statements)

References 29 publications

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“…Michel-Rostand Soumo Tchio 1 *, Saïdou Abdoulkary 2 and Alidou Mohamadou 1,3 1 Faculty of Sciences, University of Maroua, Maroua, Cameroon…”

Section: Author Detailsmentioning

confidence: 99%

“…The co-propagation of two nonlinear waves in nonlinear optical Kerr media under a slowly varying amplitude approximation is made by using extensions of the NLS equation, whose analytical results provide the dispersion relation, the unstable conditions, as well as the gain spectra. This extension of NLS equation can take into account a large variety of physical properties such as higher-orders dispersion (like third-order dispersion (TOD) and fourth-order dispersion (FOD)) [2][3][4][5][6][7][8][9]; multiple optical beams [10]; negative index material [11]; saturable nonlinearity [12]; and non-instantaneous nonlinear response [13]. Third-order dispersion is used to describe the proprieties of ultrashort pulses in the subpicosecond to femtosecond domain.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Emergence of Raman Peaks Due to Septic Nonlinearity in Noninstantaneous Kerr Media

Tchio¹,

Abdoulkary²,

Mohamadou³

2021

Nonlinear Optics - From Solitons to Similaritons

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We analyze the modulation instability induced by cross-phase modulation of two co-propagating optical beams in nonlinear fiber with the effect of higher-order dispersion and septic nonlinearity. We investigate in detail the effect of relaxation nonlinear response to the gain spectrum both in normal group velocity dispersion (GVD) and anomalous dispersion regime. We show that the walk-off, the relaxation nonlinear response time as well as the higher-order process particularly influence the generation of the modulation instability gain. Our results shows that the emerging Raman peaks is observable both in the case of weak dispersion and in a higher-order dispersion for mixed GVD regime with slow response time. These Raman peaks are shifted toward higher frequencies with the decrease of their magnitude, when the walk-off increases.

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“…Michel-Rostand Soumo Tchio 1 *, Saïdou Abdoulkary 2 and Alidou Mohamadou 1,3 1 Faculty of Sciences, University of Maroua, Maroua, Cameroon…”

Section: Author Detailsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Emergence of Raman Peaks Due to Septic Nonlinearity in Noninstantaneous Kerr Media

Tchio¹,

Abdoulkary²,

Mohamadou³

2021

Nonlinear Optics - From Solitons to Similaritons

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“…[ 23–30 ] Using nonlinear Schrö dinger equation as the model equation for slowly modulated waves propagating in NLTNs, some interesting nonlinear phenomena of NLTNs have been discovered, such as modulation instability, solitons, and rogue waves (RWs). [ 20,29,31–36 ] In recent decades, these nonlinear phenomena have undergone much theoretical and experimental research. [ 37 ] Mathematically, the concept of RWs is generally thought of as rational polynomials construct based on the integrability of a class of nonlinear partial differential equations such as the focusing nonlinear Schrödinger (NLS) equation.…”

Section: Introductionmentioning

confidence: 99%

Phase Engineering Chirped Super Rogue Waves in a Nonlinear Transmission Network with Dispersive Elements

Kengne

Liu

2021

Advcd Theory and Sims

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A discrete nonlinear transmission network with dispersive element is considered. It is shown that the dynamics of slowly modulated waves propagating in this network are governed by a generalized cubic‐quintic nonlinear Schrödinger equation with self‐steepening and self‐frequency shift. Through the baseband modulational instability (MI) analysis, the conditions for this network to support the propagation of chirped super rogue waves (SRWs) are obtained. Based on the analytical rational solutions of the governed equation, chirped first‐ and second‐order super rogue waves are engineered in the nonlinear transmission network under consideration. The effects of the dispersive elements of the network on the chirped SRWs propagating in the network system are investigated. Particularly, it is shown that the introduction of the dispersive linear capacitance of the network enhances the baseband MI and both the derived SRWs and the corresponding frequency chirp are localized in both time and space. It is also shown that the structure of the frequency chirp depends strongly on the pulse self‐steepening and self‐frequency shift.

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“…The main purpose of this work is to investigate the behavior of the dark and bright solitons by a nonlinear evolution equation with fractional order describing the waves propagation in nonlinear left-handed electrical transmission line giving by [39,40],…”

Section: Introductionmentioning

confidence: 99%

“…Thus, in this article we apply the Adomian decomposition method (ADM) to this equation ( 1) of [39,40] to study the solutions of dark and bright solitons with the effect of fractional derivatives order and initial conditions. The details of the set of nonlinear evolution equations are specified [39,40]. Here (α) is the fractional derivative order and 0 < α ≤ 1.…”

Section: Introductionmentioning

confidence: 99%

Solitary waves and modulation instability with the influence of fractional derivative order in nonlinear left-handed transmission line

et al. 2021

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The resolution of the reduced fractional nonlinear Schrödinger equation obtained from the model describing the wave propagation in the left-handed nonlinear transmission line presented by Djidere et al recently, allowed us in this work through the Adomian decomposition method (ADM) to highlight the behavior and to study the propagation process of the dark and bright soliton solutions with the effect of the fractional derivative order as well as the Modulation Instability gain spectrum (MI) in the LHNLTL. By inserting fractional derivatives

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Solitary wave solutions and modulational instability analysis of the nonlinear Schrödinger equation with higher-order nonlinear terms in the left-handed nonlinear transmission lines

Cited by 24 publications

References 29 publications

Emergence of Raman Peaks Due to Septic Nonlinearity in Noninstantaneous Kerr Media

Emergence of Raman Peaks Due to Septic Nonlinearity in Noninstantaneous Kerr Media

Phase Engineering Chirped Super Rogue Waves in a Nonlinear Transmission Network with Dispersive Elements

Solitary waves and modulation instability with the influence of fractional derivative order in nonlinear left-handed transmission line

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