Distorted light bullet in a tapered graded-index waveguide with PT symmetric potentials

Wen, Xue-Kun; Feng, Rui; Lin, Johnny Shinn‐Nan; Liu, Wei; Chen, Fang; Qian-Sheng, Yang

doi:10.1016/j.ijleo.2021.168092

Cited by 41 publications

(8 citation statements)

References 34 publications

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“…There are many methods proposed in the literature for obtaining exact solutions of differential-difference equations (D Es). Examples of these methods are, Hirota method 21 , exponential function method 22,23 , square operator method 24,25 , similarity transformation method 26,27 , and neural network methods 28 . One of the effective methods for getting exact solution of D Es such as Eqs.…”

Section: Some New Soliton Solutions Of a Semi-discrete Fractional Com...mentioning

confidence: 99%

Some new soliton solutions of a semi-discrete fractional complex coupled dispersionless system

Kader

Bialy

Nour

et al. 2023

Sci Rep

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Section: Some New Soliton Solutions Of a Semi-discrete Fractional Com...mentioning

confidence: 99%

Some new soliton solutions of a semi-discrete fractional complex coupled dispersionless system

Kader

Bialy

Nour

et al. 2023

Sci Rep

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“…Along with the existence of envelope solitons, rouge waves and breathers, there are also recently developed solutions of the NLSE. The soliton solution of a fractional order NLSE [73], one (two) soliton solution of a fifth-order NLSE [74], one (two)-soliton solutions of a coupled NLSE [75], the discrete envelope soliton solution of a time-fractional Ablowitz-Ladik model [76], envelope solitons of a three-component coupled nonlinear Schrödinger model using the neural network method [77,78], the optical solitons of a coupled NLSE using the neural network method [78], the light bullet solitons of a (3 + 1)-D normalized nonlinear Schrödinger equation [79] have been reported. Although, in our recent work, we are only restricted to study the modulational instability only.…”

Section: W + =mentioning

confidence: 99%

Modulational instability of a Yukawa fluid excitation under the Quasi-localized charged approximation (QLCA) framework

Dalui¹,

Kumar²,

Sharma³

2023

Phys. Scr.

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Collective response of a strongly coupled system departs from that in continuum phase upon transition to the quasi-crystalline phase, or a Wigner lattice. The nonlinearity driven modulational instability, for example, of a quasi-crystalline dusty plasma lattice wave, is predicted to inevitably grow macroscopic envelope structures at the expense of a mesoscopic carrier wave. The modulational instability in the dimensionally extended quasi-crystalline or amorphous phase of a strongly coupled system, uniquely accessed by the quasi-localized charge approximation (QLCA) formulation, is shown to offer conditional stability over the entire range of spectral scales by prescribing a narrower instability regime. In distinction from the excitations of linear one-dimensional chain of strongly coupled dust grains, the longitudinal modes of a quasi-crystalline phase incorporated by means of a pair correlation function in the present QLCA based treatment shows the lattice excitations to be stable for arbitrarily long wavelengths beyond a finite value of screening parameter κ = a/λ D = 0.182 at low enough temperature, where a is the inter dust separation and λ D is the plasma Debye length. However, this unstable domain of the parameter space does grow with increase in the dust temperature which invokes the weak coupling-like effect. The present results show that in comparison to the one-dimensional chains, the dimensionally extended strongly coupled lattice are potentially stable with respect to the macroscopic amplitude modulations. Results offer a greater handle over the macroscopic structures growing from the mesoscopic fluctuations, a mechanism which underlies a variety of processes, ranging from the barrier formation in strongly coupled turbulence to the highly localized modification, induced by collective excitation, of the ultracold ions trapped in strong electromagnetic fields. The existence of the growth rate of instability as well as the maximum modulational growth rate of instability has been investigated for a wide range of values of the screening parameter.

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“…Wang et al [17] used the new scheme by combining the modified Riemann-Liouville fractional derivative rule and two kinds of fractional dual-function methods with the Mittag-Leffler function on the space-time fractional Fokas-Lenells equation to find some new exact analytical solutions including bright soliton, dark soliton, combined soliton, and periodic solutions. Wen et al [18] used tapered gradedindex waveguides with parity-time-symmetric potentials to obtain the light bullet. Fang et al [19] applied the physics-informed neural network to solve a variety of femtosecond optical soliton solutions of the high-order nonlinear Schrödinger equation, including the one-soliton solution, two-soliton solution, rogue wave solution, W-soliton solution, and Msoliton solution.…”

Section: Introductionmentioning

confidence: 99%

Generalized Exp-Function Method to Find Closed Form Solutions of Nonlinear Dispersive Modified Benjamin–Bona–Mahony Equation Defined by Seismic Sea Waves

et al. 2022

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Using the new generalized exp-function method, we were able to derive significant novel closed form solutions to the nonlinear dispersive modified Benjamin–Bona–Mahony (DMBBM) equation. The general framework of the new generalized exp-function method has been given. Many novel closed form solutions have been obtained in the form of hyperbolic, trigonometric, and rational function solutions. Using the computer application Wolfram Mathematica 10, we plotted 2D, 3D, and contour surfaces of closed form solutions found in this work. In the form of a table, the acquired results are compared to the known solutions in the existing literature.

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Distorted light bullet in a tapered graded-index waveguide with PT symmetric potentials

Cited by 41 publications

References 34 publications

Some new soliton solutions of a semi-discrete fractional complex coupled dispersionless system

Some new soliton solutions of a semi-discrete fractional complex coupled dispersionless system

Modulational instability of a Yukawa fluid excitation under the Quasi-localized charged approximation (QLCA) framework

Generalized Exp-Function Method to Find Closed Form Solutions of Nonlinear Dispersive Modified Benjamin–Bona–Mahony Equation Defined by Seismic Sea Waves

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