Modulational instability in addition to discrete breathers in 2D quantum ultracold atoms loaded in optical lattices

Djoufack, Z.I.; Fotsa-Ngaffo, Fernande; Tala-Tebue, E.; Fendzi-Donfack, Emmanuel; Kapche-Tagne, F.

doi:10.1007/s11071-019-05295-w

Cited by 16 publications

(8 citation statements)

References 77 publications

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“…We observe χ BS scaling linearly with saturable parameter. Such behavior is in agreement with analytical approach, in which we follow the standard procedure for investigating the stability of a continuous wave solution [23,30]. We start by observing that the continuous version of Eq.…”

Section: Resultssupporting

confidence: 72%

“…Modulational instability refers to the stability, with respect to any perturbation, of a wave with constant amplitude that propagates through a nonlinear dispersive medium [23,24]. Such phenomenon has been widely studied in different frameworks and is usually seen as the starting point for regimes of breathing modes and localized solutions [25][26][27][28][29][30][31][32]. Significant changes in the crossover between modulational instability and breather solutions have been reported by exploring the influence of next-nearest-neighbor coupling in nonlinear discrete lattices [25].…”

Section: Introductionmentioning

confidence: 99%

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Thresholds between modulational stability, rogue waves and soliton regimes in saturable nonlinear media

et al. 2022

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We study a third-order nonlinear Schrödinger equation for a saturable nonlinear media, which can represent either optical pulse propagation in 1D nonlinear waveguide arrays or electron dynamics in onedimensional lattices. Here, we describe how stable uniform solutions can evolve into regimes in which they are localized. We analyze the existence conditions for such dynamical regimes, as well as the intermediate (breather and chaotic-like solutions). Since regimes are significantly changed by the saturable parameter, we show phase diagrams with critical nonlinear strengths separating such regimes. Numerical data and analytical approach show the nonlinear strength above which uniform solutions become breather solutions increasing with the saturation parameter. We also reveal chaoticlike solutions exhibiting clear signatures of emerging rogue waves, such as peaks showing long-tailed statistics. The thresholds of this regime are increased by the saturable nonlinearity. On the other hand, the regime of localized solutions, which are well-described by bright

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Section: Resultssupporting

confidence: 72%

Section: Introductionmentioning

confidence: 99%

Thresholds between modulational stability, rogue waves and soliton regimes in saturable nonlinear media

et al. 2022

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“…The framework for analysis is the quasi-discrete approximation with respect to long wave-length perturbations, which yields a nonlinear Schrödinger (NLS) equation. A close examination of the P and Q coefficients, as well as their product, allows us to classify the nature of the analytical solutions; such an approach proves fruitful in many physical context (see, for instance, [27]). Intriguingly, for sufficiently strong secondneighbor coupling, the lattice exhibits a non-monotonicity in its dispersion curve, and this opens up regimes where both backward-wave and forwardwave solitonic excitations can propagate at the same frequency.…”

Section: Introductionmentioning

confidence: 99%

Backward- and forward-wave soliton co-existence due to second-neighbor coupling in a left-handed transmission line

Mahmoud

Abdoulkary

English

et al. 2022

Preprint

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We study analytically and numerically the impact of the second-neighbor interactions on the propagation of an initial wave-packet through a coupled nonlinear left-handed transmission line. We start with a detailed analysis of the dispersion curve and group velocity. We then use the quasi-discrete approximation with respect to long wavelength transverse perturbations to reduce the nonlinear discrete model of the lattice to a nonlinear Schrödinger equation. A detailed analysis of the product of the group velocity dispersion (P) and the nonlinear term (Q) is presented with respect to the relevant parameters of the system. Intriguingly, we analytically observe that the product can be either simultaneously positive and negative, or positive positive, or even negative negative in different frequency bands. Our numerical results demonstrate that for sufficiently strong second-neighbor coupling, bright backward-wave pulses and dark solitons can coexist at a common frequency, and these travel in opposite directions through the lattice.PACS 05.45,Yv · 04.20.Jb · 42.65.Tg

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“…In [18] a detailed study on different physical models has been conducted. Many researchers have used the MI analysis for various models such as the nonautonomous Lenells-Fokas model [19], a variable-coefficient nonlinear Schrödinger equation with fourth-order effects [20], an integrable coupled nonlinear Schrödinger system [21], 2D quantum ultracold atoms [22], a deformed Fokas-Lenells equation [23], the coupled derivative NLS equation [24], Coupled nonlinear Schrödinger equation [25], linearly coupled complex cubic quintic Ginzburg Landau equations [26,27], the linearly-coupled NLS equations [28], an inhomogeneous NLS equation including a pseudo-stimulated-Raman-scattering term [29], perturbed nonlinear Schrödinger-Hirota equation [30], Mel'nikov system [31], Cubic-quintic nonlinear Helmholtz equation [32], coupled Zakharov-Kuznetsov [33], coupled generalized NLS equations [34] and many other equations from [35]. In 2017, Mustafa et al [36] investigated the MI analysis of the (1+1)dimensional coupled NLS equation with constant coefficients.…”

Section: Introductionmentioning

confidence: 99%

Modulation instability analysis of a nonautonomous $$(3+1)$$-dimensional coupled nonlinear Schrödinger equation

Patel

Kumar

2021

Nonlinear Dyn

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We investigate the modulation instability (MI) analysis of a nonautonomous (3+1)-dimensional coupled nonlinear Schrödinger (NLS) equation with timedependent dispersion and phase modulation coefficients. By employing standard linear stability analysis, we obtain an explicit expression for the MI gain as a function of dispersion, phase modulation, perturbation wave numbers and an initial incidence power. The nonautonomous coupled NLS equation is found to be modulationally unstable for the same sign of dispersion and phase modulation coefficients. This equation is modulationally stable for zero-dispersion and or phase modulation coefficients. But non-zero dispersion coefficient, it is modulationally stable/unstable on distinct bandwidth of wave numbers. The trigonometric, exponential, algebraic function of time and constant have been chosen as test functions for dispersion and phase modulation to find the effect on the MI analysis. The effect of focusing and defocusing medium on the MI analysis has also been investigated. The MI bandwidth in the focusing medium is found to be larger than defocusing medium. It is found that the modulation instability of the equation can be managed by proper choice of the dispersion and phase modulation parameters.

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Modulational instability in addition to discrete breathers in 2D quantum ultracold atoms loaded in optical lattices

Cited by 16 publications

References 77 publications

Thresholds between modulational stability, rogue waves and soliton regimes in saturable nonlinear media

Thresholds between modulational stability, rogue waves and soliton regimes in saturable nonlinear media

Backward- and forward-wave soliton co-existence due to second-neighbor coupling in a left-handed transmission line

Modulation instability analysis of a nonautonomous $$(3+1)$$-dimensional coupled nonlinear Schrödinger equation

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