Three-dimensional Bose–Einstein gap solitons in optical lattices with fractional diffraction

Zhiming Chen, Xiuye Liu, Hongqiang Xie and Jianhua Zeng

Chaos, Solitons & Fractals, 2024, vol. 180, issue C

Abstract: Compared with low-dimensional solitons that are widely studied in various realizable nonlinear physical systems, the properties and dynamics of three-dimensional solitons and vortices have not been well disclosed yet. Using numerical simulations and theoretical analysis, we here address the existence, structural property, and dynamics of three-dimensional gap solitons and vortices (with topological charge s=1) of Bose–Einstein condensates moving by Lévy flights (characterized by fractional diffraction operators, Lévy index 1<α≤2) in optical lattices. We stress that previously the localized modes have only been revealed in low-dimensional nonlinear fractional systems in one- and two-dimensional periodic potentials, our study presented here thus drives the associated nonlinear-wave research into three-dimensional configurations. The three-dimensional optical lattices exhibit a nontrivial wide band-gap feature, within which the matter-wave localized gap modes could be excited. The stability and instability regions of both three-dimensional gap modes are obtained via direct perturbed simulations, shedding light on multidimensional soliton physics in nonlinear fractional systems with periodic potentials.

Keywords: Three-dimensional solitons; Gap solitons and vortices; Bose–Einstein condensates; Fractional Schrödinger equation; Optical lattices (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:180:y:2024:i:c:s0960077924001097

DOI: 10.1016/j.chaos.2024.114558

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