Peregrine Solitons of the Higher-Order, Inhomogeneous, Coupled, Discrete, and Nonlocal Nonlinear Schrödinger Equations

Uthayakumar, T.; Sakkaf, Laila Al; Khawaja, U. Al

doi:10.3389/fphy.2020.596886

Cited by 7 publications

(2 citation statements)

References 292 publications

(256 reference statements)

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“…In optical fiber communications, Solitons can be viewed as localized pulses in time or bounded self-guided beams in space [6]. The propagation of optical solitons is governed by the nonlinear Schrödinger (NLS) equation [7,8]:…”

Section: Introductionmentioning

confidence: 99%

Multi-soliton solutions and asymptotic analysis for the coupled variable-coefficient Lakshmanan-Porsezian-Daniel equations via Riemann-Hilbert approach

Ма¹,

Li²,

Wang³

et al. 2023

Phys. Scr.

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In this paper, we study multi-soliton solutions and asymptotic analysis for the coupled variable-coefficient Lakshmanan-Porsezian-Daniel equations, which describe the simultaneous propagation of nonlinear waves in the inhomogeneous optical fibers. We analyze the spectrum of the Lax pair to establish the Riemann-Hilbert problem. Using such Riemann-Hilbert problem, we calculate various multi-soliton solutions without reflection, including breather-like and mixed solitons. We illustrate the propagation and interaction dynamics of the solitons through appropriate parameter selection and asymptotic analysis. We find that the interaction between solitons is elastic, the amplitudes of solitons are only determined by the initial velocity and interaction, and the soliton with lower energy always yields a position shift when elastic interaction occurs. In addition, we observe that the existence time of the wave changes with energy and that multiple elastic interactions between solitons can be obtained when we choose appropriate variable coefficients. Then, we investigate the influences of group velocity dispersions and fourth-order dispersions on the interactions of solitons through parameter modulation mode and asymptotic analysis. Furthermore, we present several new types of nonlinear phenomena graphically, including elastic interactions between parabolic solitons and hump-type solitons, elastic interactions between cubic solitons and hump-type solitons, and periodic-changing propagations.

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Section: Introductionmentioning

confidence: 99%

Multi-soliton solutions and asymptotic analysis for the coupled variable-coefficient Lakshmanan-Porsezian-Daniel equations via Riemann-Hilbert approach

Ма¹,

Li²,

Wang³

et al. 2023

Phys. Scr.

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show abstract

“…In [17,[22][23][24][25][26][27], the dynamics of non-autonomous solitons like width variation and energy control are discussed by varying the dispersion, nonlinearity and gain/loss parameters. The propagation of non-autonomous solitons and tunneling in a optical fiber are discussed in [19,25].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear tunneling of solitons in a variable coefficients nonlinear Schrödinger equation with $\mathcal{PT}$-symmetric Rosen-Morse potential

Manikandan,

Sudharsan,

Senthilvelan

2021

Preprint

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We construct soliton solution of a variable coefficients nonlinear Schrödinger equation in the presence of parity reflection -time reversal (PT )− symmetric Rosen-Morse potential using similarity transformation technique. We transform the variable coefficients nonlinear Schrödinger equation into the nonlinear Schrödinger equation with PT −symmetric potential with certain integrability conditions. We investigate in-detail the features of the obtained soliton solutions with two different forms of dispersion parameters. Further, we analyze the nonlinear tunneling effect of soliton profiles by considering two different forms of nonlinear barrier/well and dispersion barrier/well. Our results show that the soliton can tunnel through nonlinear barrier/well and dispersion barrier/well with enlarged and suppressed amplitudes depending on the sign of the height. Our theoretical findings are experimentally realizable and might help to model the optical devices.

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Dynamical optical soliton solutions and behavior for the nonlinear Schrödinger equation with Kudryashov’s quintuple power law of refractive index together with the dual-form of nonlocal nonlinearity

Ashraf,

Seadawy,

Rizvi

et al. 2024

Opt Quant Electron

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Peregrine Solitons of the Higher-Order, Inhomogeneous, Coupled, Discrete, and Nonlocal Nonlinear Schrödinger Equations

Cited by 7 publications

References 292 publications

Multi-soliton solutions and asymptotic analysis for the coupled variable-coefficient Lakshmanan-Porsezian-Daniel equations via Riemann-Hilbert approach

Multi-soliton solutions and asymptotic analysis for the coupled variable-coefficient Lakshmanan-Porsezian-Daniel equations via Riemann-Hilbert approach

Nonlinear tunneling of solitons in a variable coefficients nonlinear Schrödinger equation with $\mathcal{PT}$-symmetric Rosen-Morse potential

Dynamical optical soliton solutions and behavior for the nonlinear Schrödinger equation with Kudryashov’s quintuple power law of refractive index together with the dual-form of nonlocal nonlinearity

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