Journal ArticleDOI
Prediction and dynamical evolution of multipole soliton families in fractional Schrödinger equation with the PT-symmetric potential and saturable nonlinearity
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This article is published in Nonlinear Dynamics.The article was published on 2022-09-27. It has received 48 citations till now. The article focuses on the topics: Multipole expansion & Soliton.read more
Citations
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Dynamics and spectral analysis of optical rogue waves for a coupled nonlinear Schrödinger equation applicable to pulse propagation in isotropic media
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A family of nonlinear Schrodinger equations and their solitons solutions
Rami Ahmad El-Nabulsi,W. Anukool +1 more
TL;DR: In this paper , three different forms of fractional nonlinear Schrödinger equations have been constructed based on the notion of nonlocal generalized fractional momentum operator, the fractional expansion Riccati method and the concept of Laplacian operator in fractal dimensions.
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Dynamics of soliton solutions in optical fibers modelled by perturbed nonlinear Schrödinger equation and stability analysis
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Predicting nonlinear dynamics of optical solitons in optical fiber via the SCPINN
TL;DR: The strongly-constrained physics-informed neural network (SCPINN) as discussed by the authors was proposed by adding the information of compound derivative embedded into the soft-consstraint of PINN to predict nonlinear dynamics and the formation process of bright and dark picosecond optical solitons, and femtosecond soliton molecule in the single-mode fiber, and reveal the variation of physical quantities including the energy, amplitude, spectrum and phase of pulses during the soliton transmission.
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Bifurcation analysis, stationary optical solitons and exact solutions for generalized nonlinear Schrödinger equation with nonlinear chromatic dispersion and quintuple power-law of refractive index in optical fibres
Tianyong Han,Zhao Li,Chenyu Li +2 more
TL;DR: In this paper , the bifurcation, stationary optical solitons and exact solutions in optical fiber propagation are studied, and the results provide a method to further study stationary optical cositons.
References
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Journal ArticleDOI
Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
TL;DR: The condition of self-adjointness as discussed by the authors ensures that the eigenvalues of a Hamiltonian are real and bounded below, replacing this condition by the weaker condition of $\mathrm{PT}$ symmetry, one obtains new infinite classes of complex Hamiltonians whose spectra are also real and positive.
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Making sense of non-Hermitian Hamiltonians
TL;DR: In this article, an alternative formulation of quantum mechanics in which the mathematical axiom of Hermiticity (transpose + complex conjugate) is replaced by the physically transparent condition of space?time reflection ( ) symmetry.
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Complex extension of quantum mechanics
TL;DR: If PT symmetry is not spontaneously broken, it is possible to construct a previously unnoticed symmetry C of the Hamiltonian, and this work is not in conflict with conventional quantum mechanics but is rather a complex generalization of it.
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Fractional Schrödinger equation.
TL;DR: The Hermiticity of the fractional Hamilton operator and the parity conservation law for fractional quantum mechanics are established and the energy spectra of a hydrogenlike atom and of a fractional oscillator in the semiclassical approximation are found.
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Fractional quantum mechanics and Lévy path integrals
TL;DR: In this article, a new extension of a fractality concept in quantum physics has been developed and path integrals over the Levy paths are defined and fractional quantum and statistical mechanics have been developed via new fractional path integral approach.