Multipole gap solitons in fractional Schrödinger equation with parity-time-symmetric optical lattices.

Abstract

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.