We discover a series of ring and cluster solitons in the (1+2)-dimensional nonlocal nonlinear fractional Schrödinger equation by iteration algorithm, and verify their robustness by introducing random perturbations during propagations. We obtain the relations between the soliton power, the orbital angular momentum, and the rotation period of phase, which are dependent on the Lévy index α. When the radial number p = 0, the soliton shapes slightly vary with the change of Lévy index. However, when p ≥ 1, the solitons exhibit novel structures, the outer ring (hump) of such solitons decrease as the Lévy index decreases. Our results extend the study of vortex and cluster solitons into fractional systems and deepen the understanding of fractional dimensions.

中文翻译：

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非局部非线性分数薛定ding方程中的涡旋和簇孤子

我们通过迭代算法在（1 + 2）维非局部非线性分数阶Schrödinger方程中发现了一系列环和簇孤子，并通过在传播过程中引入随机扰动来验证其鲁棒性。我们获得了孤子力，轨道角动量和相位旋转周期之间的关系，这些关系取决于Lévy指数α。当径向数p = 0时，孤子形状随Lévy指数的变化而略有变化。但是，当p≥1时，孤子呈现出新颖的结构，随着Lévy指数的降低，此类孤子的外环（驼峰）会减小。我们的结果将涡旋和团簇孤子的研究扩展到分数系统中，并加深了对分数维的理解。