Second-harmonic generation in the system with fractional diffraction

Article Mathematics, Interdisciplinary Applications

Quadratic fractional solitons

Liangwei Zeng et al.

Summary: This paper introduces a system combining nonlinear effects and fractional diffraction, investigates different types of soliton structures formed under varying parameters, and analyzes their stability and instability.

CHAOS SOLITONS & FRACTALS (2022)

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Article Engineering, Mechanical

Families of gap solitons and their complexes in media with saturable nonlinearity and fractional diffraction

Liangwei Zeng et al.

Summary: We have demonstrated the existence of various types of gap localized modes, including one- and two-dimensional solitons and soliton clusters, as well as vortex modes, in optical media with saturable Kerr nonlinearity and fractional diffraction. We found that soliton clusters with different peak numbers can be stable, and the localized modes at the center of the first and second band gaps are stable. The stability of these modes is confirmed through linear stability analysis and numerical simulations.

NONLINEAR DYNAMICS (2022)

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Article Mathematics, Interdisciplinary Applications

Transformation of multipole and vortex solitons in the nonlocal nonlinear fractional Schrodinger equation by means of Levy-index management

Qing Wang et al.

Summary: The structure and stability of multipole and vortex solitons in the nonlocal nonlinear fractional Schrodinger equation are numerically studied, and it is found that the solitons compress with the decrease of Levy index, leading to the formation of new stable modes.

CHAOS SOLITONS & FRACTALS (2022)

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Article Mathematics, Interdisciplinary Applications

Conical diffraction modulation in fractional dimensions with a PT-symmetric potential

Zhenkun Wu et al.

Summary: This study analyzes conical diffraction in space-fractional parity-time (PT) symmetry and examines the peculiar characteristics of the corresponding Floquet Bloch modes. The study finds that the band structure in this model is different from regular PT symmetry, and the linear band structure during propagation has unique properties.

CHAOS SOLITONS & FRACTALS (2022)

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Article Physics, Fluids & Plasmas

Domain walls in fractional media

Shatrughna Kumar et al.

Summary: This study focuses on the analysis of optical and matter-wave modes supported by fractional diffraction in nonlinear media. A new type of such states, called domain walls in the immiscible fields, is predicted. Numerical study confirms the existence and stability of these domain walls, as well as provides analytical results for their width scaling. Asymmetric domain walls are also constructed in the system with unequal diffraction coefficients and/or different Levy indices.

PHYSICAL REVIEW E (2022)

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Article Mathematics, Interdisciplinary Applications

Solitons in spin-orbit-coupled systems with fractional spatial derivatives

Liangwei Zeng et al.

Summary: This study demonstrates the existence of various types of solitons in spin-orbit-coupled systems with fractional dimensions based on Levy random flights, and finds that the Levy index, self-and cross-phase modulation strength, and propagation constant strongly affect the waveforms and stability of solitons; the research concludes that solitons tend to be stable when the Levy index is close to 2, while they tend to be unstable when the Levy index is close to 1.

CHAOS SOLITONS & FRACTALS (2021)

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Article Optics

Symmetry-breaking bifurcations and ghost states in the fractional nonlinear Schrodinger equation with a PT-symmetric potential

Pengfei Li et al.

Summary: The study investigates symmetry-breaking and restoring bifurcations of solitons in a fractional Schrodinger equation, especially in the presence of CQ nonlinearity and a parity-time-symmetric potential. Solitons destabilize at the bifurcation point, but stability is restored through an inverse bifurcation in the case of CQ nonlinearity. Two mutually conjugate branches of ghost states are created in the presence of fractional diffraction.

OPTICS LETTERS (2021)

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Review Optics

Optical Solitons and Vortices in Fractional Media: A Mini-Review of Recent Results

Boris A. Malomed

Summary: The article reviews recent results on stable propagation of solitons and solitary vortices in models based on the NLSE, including fractional diffraction and nonlinear terms. The results are mainly numerical, with some analytical findings included for fast moving solitons. The article also briefly considers dissipative solitons governed by the fractional complex Ginzburg-Landau equation.

PHOTONICS (2021)

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Article Engineering, Mechanical

Stable and oscillating solitons of PT-symmetric couplers with gain and loss in fractional dimension

Liangwei Zeng et al.

Summary: This study reports families of coupled solitons in PT-symmetric physical models with gain and loss in fractional dimension, both with and without cross-interactions modulation (CIM). The obtained PT-symmetric coupled solitons are investigated in terms of profiles, powers, stability areas, and propagation dynamics. It is found that the stability area of the model with CIM is broader compared to the one without CIM, and oscillating PT-symmetric coupled solitons can also exist in the CIM model with the same coefficients of the self- and cross-interactions modulations. Additionally, the period of these oscillating coupled solitons can be controlled by the linear coupling coefficient.

NONLINEAR DYNAMICS (2021)

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Article Mathematics, Interdisciplinary Applications

Soliton dynamics in a fractional complex Ginzburg-Landau model

Yunli Qiu et al.

CHAOS SOLITONS & FRACTALS (2020)

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Article Mathematics, Interdisciplinary Applications

Symmetry breaking of spatial Kerr solitons in fractional dimension

Pengfei Li et al.

CHAOS SOLITONS & FRACTALS (2020)

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Article Optics

Multipole gap solitons in fractional Schrodinger equation with parity-time-symmetric optical lattices

Xing Zhu et al.

OPTICS EXPRESS (2020)

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The fractional discrete nonlinear Schrodinger equation

Mario Molina

PHYSICS LETTERS A (2020)

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Vector optical soliton and periodic solutions of a coupled fractional nonlinear Schrodinger equation

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Junbo Chen et al.

CHAOS (2020)

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Vortex solitons in fractional nonlinear Schrodinger equation with the cubic-quintic nonlinearity

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Fractional quantum couplers

Liangwei Zeng et al.

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Stabilization of single- and multi-peak solitons in the fractional nonlinear Schrodinger equation with a trapping potential

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One-dimensional solitons in fractional Schrodinger equation with a spatially periodical modulated nonlinearity: nonlinear lattice

Liangwei Zeng et al.

OPTICS LETTERS (2019)

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ON RIESZ DERIVATIVE

Min Cai et al.

FRACTIONAL CALCULUS AND APPLIED ANALYSIS (2019)

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Variational approach for breathers in a nonlinear fractional Schrodinger equation

Manna Chen et al.

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION (2019)

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Vortex solitons in fractional systems with partially parity-time-symmetric azimuthal potentials

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NONLINEAR DYNAMICS (2019)

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Dissipative surface solitons in a nonlinear fractional Schrodinger equation

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OPTICS LETTERS (2019)

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Surface gap solitons in a nonlinear fractional Schrodinger equation

Jing Xiao et al.

OPTICS EXPRESS (2018)

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Double-hump solitons in fractional dimensions with a PT-symmetric potential

Liangwei Dong et al.

OPTICS EXPRESS (2018)

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Composition Relation between Nonlinear Bloch Waves and Gap Solitons in Periodic Fractional Systems

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Solitons in the fractional Schrodinger equation with parity-time-symmetric lattice potential

Xiankun Yao et al.

PHOTONICS RESEARCH (2018)

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Xiankun Yao et al.

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Wei-Ping Zhong et al.

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Stefano Longhi

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PHYSICAL REVIEW B (2015)

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Vortical light bullets in second-harmonic-generating media supported by a trapping potential

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JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL (2007)

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Second-harmonic generation in the system with fractional diffraction

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