Vortex and cluster solitons in nonlocal nonlinear fractional Schrodinger equation

We discover a series of ring and cluster solitons in the (1+2)-dimensional nonlocal nonlinear fractional Schrodinger 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 Levy index alpha. When the radial number p = 0, the soliton shapes slightly vary with the change of Levy index. However, when p >= 1, the solitons exhibit novel structures, the outer ring (hump) of such solitons decrease as the Levy index decreases. Our results extend the study of vortex and cluster solitons into fractional systems and deepen the understanding of fractional dimensions.