Vortex and cluster solitons in nonlocal nonlinear fractional Schrödinger equation
Qing Wang, Guo Liang
Abstract
Abstract 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.