We investigate new types of gap solitons in a periodic parity-time (PT)-symmetric lattice with fractional-order diffraction. Both the fundamental and dipole solitons in the first and second gaps are discussed. It is found that fractional-order diffraction can not only stabilize low-power dipole PT solitons in the first gap under focusing nonlinearity, but also help to get stable dipole PT solitons in the second gap under defocusing nonlinearity. Additionally, the influence of the strength ${w_i}$ of the gain–loss component on the properties of solitons is also analyzed. It is shown that increasing ${w_i}$ is unfavorable to the stability of fractional fundamental solitons, especially for the second gap, while for fractional dipole solitons, the increase of ${w_i}$ may lead to their destabilization in the first gap, but stabilization in the second gap.

中文翻译：

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奇偶时间对称格中具有分数阶衍射的间隙孤子

我们用分数阶衍射研究周期性奇偶时间（PT）对称晶格中的新型间隙孤子。讨论了第一和第二间隙中的基极和偶极孤子。发现分数阶衍射不仅可以在聚焦非线性下稳定第一间隙中的低功率偶极PT孤子，而且还可以在散焦非线性下获得第二间隙中的稳定偶极PT孤子。此外，还分析了增益损耗分量的强度$ {w_i} $对孤子特性的影响。结果表明，增加$ {w_i} $不利于分数基孤子的稳定性，特别是对于第二个缺口，而分数偶极子孤子的$ {w_i} $的增加 可能会导致它们在第一个缺口中不稳定，但会在第二个缺口中稳定。