We investigate the existence and stability of in-phase three-pole and four-pole gap solitons in the fractional Schrödinger equation supported by one-dimensional parity-time-symmetric periodic potentials (optical lattices) with defocusing Kerr nonlinearity. These solitons exist in the first finite gap and are stable in the moderate power region. When the Lévy index decreases, the stable regions of these in-phase multipole gap solitons shrink. Below a Lévy index threshold, the effective multipole soliton widths decrease as the Lévy index increases. Above the threshold, these solitons become less localized as the Lévy index increases. The Lévy index cannot change the phase transition point of the PT-symmetric optical lattices. We also study transverse power flow in these multipole gap solitons.
We report on the existence and stability of mixed-gap vector surface solitons at the interface between a uniform medium and an optical lattice with fractional-order diffraction. Two components of these vector surface solitons arise from the semi-infinite and the first finite gaps of the optical lattices, respectively. It is found that the mixed-gap vector surface solitons can be stable in the nonlinear fractional Schrödinger equations. For some propagation constants of the first component, the stability domain of these vector surface solitons can also be widened by decreasing the Lévy index. Moreover, we also perform stability analysis on the vector surface solitons, and it is corroborated by the propagations of the perturbed vector surface solitons.
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