Centrosymmetric multipole solitons with fractional-order diffraction in two-dimensional parity-time-symmetric optical lattices

IF 2.7 3区 数学 Q1 MATHEMATICS, APPLIED Physica D: Nonlinear Phenomena Pub Date : 2024-09-12 DOI:10.1016/j.physd.2024.134379
Xing Zhu , Milivoj R. Belić , Dumitru Mihalache , Dewen Cao , Liangwei Zeng
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Abstract

Multipole solitons in higher-dimensional nonlinear Schrödinger equation with fractional diffraction are of high current interest. This paper studies multipole gap solitons in parity-time (PT)-symmetric lattices with fractional diffraction. The results obtained demonstrate that both on-site and off-site eight-pole solitons with fractional-order diffraction can be stabilized in a two-dimensional (2D) PT-symmetric optical lattice with defocusing Kerr nonlinearity. These solitons are in-phase and centrosymmetric. On-site eight-pole solitons propagate in a square formation, while off-site solitons propagate in a two-by-four formation. Both on-site and off-site solitons are found to be stable within a low-power range in the first band gap. As the Lévy index decreases, the stability regions of both on-site and off-site solitons narrow. Off-site eight-pole solitons can approach the lower edge of the first Bloch band, whereas on-site eight-pole solitons cannot. Additionally, we investigate the transverse power flow vector of these multipole gap solitons, illustrating the transverse energy flow from gain to loss regions.

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二维奇偶时对称光晶格中具有分数阶衍射的中心对称多极孤子
当前,具有分数衍射的高维非线性薛定谔方程中的多极孤子备受关注。本文研究了具有分数衍射的奇偶时(PT)对称晶格中的多极间隙孤子。研究结果表明,具有分数阶衍射的现场和非现场八极孤子都能在具有离焦克尔非线性的二维(2D)PT 对称光学晶格中稳定下来。这些孤子是同相和中心对称的。场内八极孤子以正方形阵型传播,场外孤子以二乘四阵型传播。在第一带隙的低功率范围内,现场和非现场孤子都是稳定的。随着莱维指数的降低,现场和非现场孤子的稳定区域都会缩小。非现场八极孤子可以接近第一布洛赫带的下边缘,而现场八极孤子则不能。此外,我们还研究了这些多极间隙孤子的横向功率流矢量,说明了从增益区到损耗区的横向能量流。
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来源期刊
Physica D: Nonlinear Phenomena
Physica D: Nonlinear Phenomena 物理-物理:数学物理
CiteScore
7.30
自引率
7.50%
发文量
213
审稿时长
65 days
期刊介绍: Physica D (Nonlinear Phenomena) publishes research and review articles reporting on experimental and theoretical works, techniques and ideas that advance the understanding of nonlinear phenomena. Topics encompass wave motion in physical, chemical and biological systems; physical or biological phenomena governed by nonlinear field equations, including hydrodynamics and turbulence; pattern formation and cooperative phenomena; instability, bifurcations, chaos, and space-time disorder; integrable/Hamiltonian systems; asymptotic analysis and, more generally, mathematical methods for nonlinear systems.
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