We demonstrate the existence of various types of solitons in the spin-orbit-coupled systems with the fractional dimension based on Lévy random flights, including the systems with or without Zeeman splitting. Specifically, the systems without Zeeman splitting can support families of symmetric solitons, whereas the systems with Zeeman splitting can support families of stable asymmetric solitons. These coupled solitons may come in the form of fundamental single solitons or dipole solitons. The Lévy index, the strength of self- and cross-phase modulation, and the propagation constant strongly affect the waveforms and stability domains of coupled solitons. The stability and instability domains of such single and dipole solitons are calculated by the method of linear stability analysis and are confirmed by the numerical simulation of perturbed propagation. The general conclusion is that for the Lévy index close to 2, corresponding to the normal nonlinear optics, the solitons tend to be stable, while in the opposite case of Lévy index close to 1, corresponding to Cauchy random flights, the solitons tend to become unstable.

我们证明了在具有基于 Lévy 随机飞行的分数维的自旋轨道耦合系统中存在各种类型的孤子，包括有或没有塞曼分裂的系统。具体来说，没有塞曼分裂的系统可以支持对称孤子族，而有塞曼分裂的系统可以支持稳定的非对称孤子族。这些耦合孤子可能以基本单孤子或偶极孤子的形式出现。Lévy 指数、自相位调制和交叉相位调制的强度以及传播常数强烈影响耦合孤子的波形和稳定性域。这种单极子和偶极子孤子的稳定性和不稳定域是通过线性稳定性分析的方法计算出来的，并通过扰动传播的数值模拟得到证实。一般的结论是，对于接近 2 的 Lévy 指数，对应于正常非线性光学，孤子趋于稳定，而在 Lévy 指数接近 1 的相反情况下，对应于柯西随机飞行，孤子趋于成为不稳定。