Symmetry-breaking bifurcations and ghost states in the fractional nonlinear Schrödinger equation with a PT-symmetric potential

We report symmetry-breaking and restoring bifurcations of solitons in a fractional Schrödinger equation with cubic or cubic–quintic (CQ) nonlinearity parity–time-symmetric potential, which may be realized optical cavities. Solitons are destabilized at the bifurcation point, and, case CQ nonlinearity, stability is restored by an inverse bifurcation. Two mutually conjugate branches ghost states (GSs), complex propagation constants, created bifurcation, solely diffraction. While GSs not true solutions, direct simulations confirm that their shapes results analysis provide “blueprint” for evolution genuine localized modes system.