The properties of existence and stability of gray solitons in parity-time (PT)-symmetric localized potentials with fractional-order diffraction are studied. This system can support stable gray solitons. The influences of the Lévy index and the real and imaginary parts of the complex potentials on existence, stability, and grayness of these solitons are carefully investigated. Especially, if some coefficients of PT-symmetric potentials in nonlinear fractional Schrödinger equation are changed, the transition between gray soliton and anti-dark soliton will occur. In addition, we also discuss the transverse energy flow in the gray and anti-dark solitons with fractional-order diffraction.

研究了具有分数阶衍射的奇偶时间(PT)对称局域势中灰色孤子的存在性和稳定性。该系统可以支持稳定的灰色孤子。仔细研究了 Lévy 指数和复势的实部和虚部对这些孤子的存在性、稳定性和灰度的影响。特别是，如果改变非线性分数阶薛定谔方程中 PT 对称势的某些系数，就会发生灰孤子和反暗孤子之间的转变。此外，我们还讨论了具有分数阶衍射的灰色和反暗孤子中的横向能流。