Dynamical behaviors of optical solitons in parity–time (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mi mathvariant="script">PT</mml:mi></mml:math>) symmetric sextic anharmonic double-well potentials

Wen, Zichao; Yan, Zhenya

doi:10.1016/j.physleta.2015.06.034

Cited by 46 publications

(16 citation statements)

References 47 publications

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“…Equation (1) becomes the usual higher-order NLS equation in the absence of the gain-and-loss distribution 53 . Equation (1) with β = 0 becomes the -symmetric nonlinear model, which has been studied 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 . In the following we consider the case in the presence of TOD term ( β ≠ 0) and gain-and-loss distribution.…”

Section: Resultsmentioning

confidence: 99%

“… 20 first introduced the complex -symmetric potentials in the NLS model such that some novel phenomena with stable modes were found. After that, a variety of distinguishing -symmetric or non- -symmetric potentials were introduced to the continuous or discrete NLS equations to explore dynamical behaviors of -symmetric nonlinear modes (see, e.g., refs 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 and references therein). Meanwhile, more and more physical experiments have also been designed to observe new wave phenomena in the sense of non-Hermitian -symmetric potentials 43 44 45 46 47 48 .…”

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confidence: 99%

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Solitonic dynamics and excitations of the nonlinear Schrödinger equation with third-order dispersion in non-Hermitian PT-symmetric potentials

Chen

Yan

2016

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Solitons are of the important significant in many fields of nonlinear science such as nonlinear optics, Bose-Einstein condensates, plamas physics, biology, fluid mechanics, and etc. The stable solitons have been captured not only theoretically and experimentally in both linear and nonlinear Schrödinger (NLS) equations in the presence of non-Hermitian potentials since the concept of the parity-time -symmetry was introduced in 1998. In this paper, we present novel bright solitons of the NLS equation with third-order dispersion in some complex -symmetric potentials (e.g., physically relevant -symmetric Scarff-II-like and harmonic-Gaussian potentials). We find stable nonlinear modes even if the respective linear -symmetric phases are broken. Moreover, we also use the adiabatic changes of the control parameters to excite the initial modes related to exact solitons to reach stable nonlinear modes. The elastic interactions of two solitons are exhibited in the third-order NLS equation with -symmetric potentials. Our results predict the dynamical phenomena of soliton equations in the presence of third-order dispersion and -symmetric potentials arising in nonlinear fiber optics and other physically relevant fields.

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Section: Resultsmentioning

confidence: 99%

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confidence: 99%

Solitonic dynamics and excitations of the nonlinear Schrödinger equation with third-order dispersion in non-Hermitian PT-symmetric potentials

Chen

Yan

2016

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“…The double-well anharmonic oscillator (DWAO) holds a great importance because of its relation to many problems of quantum chemistry and field theory [1][2][3][4]. Dai-Nam Le et al was studied the Schrödinger equation for the purely sextic double-well potential problem in twodimensional space by wave function ansatz method for analytical approach and by Feranchuk-Komarov operator method for numerical approach [1].…”

Section: Introductionmentioning

confidence: 99%

A Theoretical Investigation of the Schrödinger Equation for a Modified Two Dimensional Purely Sextic Double-Well Potential

Maireche¹

2021

Yanbu Journal of Engineering and Science

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A theoretical analytical investigation for the exact solvability of non-relativistic quantum spectrum systems, at low energy for modified two-dimensional purely sextic double-well potential (2D-modified sextic DWAO potential) is discussed, by means Bopp's shift method, instead to solving deformed Schrödinger equation with star product, in the framework of both noncommutativite two dimensional real space and phase (NC: 2D-RSP), the exact corrections for lowest excitations are found straightforwardly for interactions in one-electron atoms by means of the standard perturbation theory for three special cases. Furthermore, the obtained corrections of energies are depended on the four infinitesimals parameters (  ,  ) and ( ,  ),

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“…However, as the Hamiltonian satisfies parity-time (PT) symmetry, its eigenvalues are real [41]. The concept of non-Hermite can be extended to the regime of optics [42,43], and then the refractive index of PT-symmetric system obeys n(r) = n × (−r) [44][45][46][47][48]. PT-symmetric systems could induce many unique optical properties, including unidirectional invisibility [49], optical transparency [43,50], power oscillations [51], and the lateral shift of reflected light beam [52].…”

Section: Introductionmentioning

confidence: 99%

Low Threshold Optical Bistability in Aperiodic PT-Symmetric Lattices Composited with Fibonacci Sequence Dielectrics and Graphene

Zhao

Guo

et al. 2019

Applied Sciences

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We explore the optical bistability in aperiodic parity–time-symmetric (PT-symmetric) photonic lattices that are composed of Fibonacci sequence dielectrics and graphene at terahertz frequencies. Two Fibonacci sequence dielectrics, viz. aperiodic photonic lattices, are utilized for enhancing band-edge resonances and achieving the electric field localization that can enhance the nonlinearity of graphene. Modulating the gain-loss factor of dielectrics in the PT symmetry lattices further strengthens the nonlinearity effect and, consequently, low threshold bistability is realized. The interval between the upper and lower bistability thresholds enlarges as the momentum relaxation time of graphene changes. Moreover, we show that the bistability threshold can also be flexibly tuned by modulating the graphene chemical potential. The study might be applied in photomemories and optical switches.

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Dynamical behaviors of optical solitons in parity–time (PT) symmetric sextic anharmonic double-well potentials

Cited by 46 publications

References 47 publications

Solitonic dynamics and excitations of the nonlinear Schrödinger equation with third-order dispersion in non-Hermitian PT-symmetric potentials

Solitonic dynamics and excitations of the nonlinear Schrödinger equation with third-order dispersion in non-Hermitian PT-symmetric potentials

A Theoretical Investigation of the Schrödinger Equation for a Modified Two Dimensional Purely Sextic Double-Well Potential

Low Threshold Optical Bistability in Aperiodic PT-Symmetric Lattices Composited with Fibonacci Sequence Dielectrics and Graphene

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