Finite Dimensional Global Attractor for a Fractional Schrödinger Type Equation with Mixed Anisotropic Dispersion

Alouini, Brahim

doi:10.1007/s10884-020-09938-0

Cited by 5 publications

(2 citation statements)

References 28 publications

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“…In a semi-classical analysis of the fractional Schrödinger equation, it is shown that the non-negative continuous potential can decay arbitrarily [6]. The fractional Schrödinger equation is still the subject of many ongoing studies [1,[7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Petviashvili Method for the Fractional Schrödinger Equation

et al. 2022

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In this paper, we extend the Petviashvili method (PM) to the fractional nonlinear Schrödinger equation (fNLSE) for the construction and analysis of its soliton solutions. We also investigate the temporal dynamics and stabilities of the soliton solutions of the fNLSE by implementing a spectral method, in which the fractional-order spectral derivatives are computed using FFT (Fast Fourier Transform) routines, and the time integration is performed by a 4th order Runge–Kutta time-stepping algorithm. We discuss the effects of the order of the fractional derivative, α, on the properties, shapes, and temporal dynamics of the soliton solutions of the fNLSE. We also examine the interaction of those soliton solutions with zero, photorefractive and q-deformed Rosen–Morse potentials. We show that for all of these potentials, the soliton solutions of the fNLSE exhibit a splitting and spreading behavior, yet their dynamics can be altered by the different forms of the potentials and noise considered.

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Section: Introductionmentioning

confidence: 99%

Petviashvili Method for the Fractional Schrödinger Equation

et al. 2022

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“…In a semi-classical analysis of the fractional Schrödinger equation, it is shown that the non-negative continuous potential can decay arbitrarily [29]. Various studies on fractional Schrödinger equation is still the subject of many different ongoing studies [24,[30][31][32].…”

Section: Introductionmentioning

confidence: 99%

Petviashvili Method for the Fractional Schrödinger Equation

Bayındır¹,

Farazande²

2021

Preprint

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In this paper, we extend the Petviashvili method (PM) to the fractional nonlinear Schrödinger equation (fNLSE) for the construction and analysis of its soliton solutions. We also investigate the temporal dynamics and stabilities of the soliton solutions of the fNLSE by implementing a spectral method, in which the fractional-order spectral derivatives are computed using FFT routines, and the time integration is performed by a 4 th order Runge-Kutta time-stepping algorithm. We discuss the effects of the order of the fractional derivative, α, on the properties, shapes, and temporal dynamics of the solitons solutions of the fNLSE. We also examine the interaction of those soliton solutions with zero, photorefractive and q-deformed Rosen-Morse potentials. We show that for all of these potentials the soliton solutions of the fNLSE exhibit a splitting and spreading behavior, yet their dynamics can be altered by the different forms of the potentials considered. The splitting and spreading dynamics of the solitons of the fNLSE are not affected by noise. Our results also indicate that the Savitzky-Golay filter can be used for the denoising of the solitons of the fNLSE.

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Existence, exponential mixing and convergence of periodic measures of fractional stochastic delay reaction-diffusion equations on Rn

Chen

Wang²

2022

Journal of Differential Equations

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Finite Dimensional Global Attractor for a Fractional Schrödinger Type Equation with Mixed Anisotropic Dispersion

Cited by 5 publications

References 28 publications

Petviashvili Method for the Fractional Schrödinger Equation

Petviashvili Method for the Fractional Schrödinger Equation

Petviashvili Method for the Fractional Schrödinger Equation

Existence, exponential mixing and convergence of periodic measures of fractional stochastic delay reaction-diffusion equations on Rn

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