Fractional-order gap solitons in spin–orbit coupling Bose–Einstein condensate with a honeycomb optical lattice

Xi Zhao, Pu Tu, Bao-Long Xi, Kai-Hua Shao, Jin-Ming Gou, Zhong-Hong Xi and Yu-Ren Shi

Chaos, Solitons & Fractals, 2026, vol. 210, issue P2

Abstract: We study the characteristics of gap solitons in spin–orbit coupling Bose–Einstein condensate (SOC-BEC) with a honeycomb optical lattice, within the theoretical framework of the fractional nonlinear Schrödinger equation. Our numerical findings show that the influence of the Lévy index on gap solitons localization is not always non-monotonic. Specifically, in the case of unipole gap solitons that are excited within a semi-infinite gap, it increases monotonically. The stability of gap solitons is the primary focus of this study. For the semi-infinite gap, higher Lévy index tends to weaken the stability of the solitons. Within a certain range of the Lévy index, increasing SOC strength improves the stability of unipole solitons, while for dipole ones, the stability improvement exhibits a non-monotonic dependence and can be achieved with either weaker or stronger SOC strength. In the first gap, the unstable region of unipole solitons shrinks significantly, mainly appearing where the SOC strength and Lévy index are relatively large. For dipole gap solitons, within the regime of small Lévy index, enhancing SOC strength improves their stability. Conversely, larger Lévy index leads to instability. Furthermore, within this region, the stability of the solitons is insensitive to variations in SOC. These results may prove valuable for exploring localized structures in fractional nonlinear systems.

Keywords: Spin–orbit coupling Bose–Einstein condensate; Fractional-order gap soliton; Honeycomb optical lattice (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:210:y:2026:i:p2:s0960077926008556

DOI: 10.1016/j.chaos.2026.118714

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