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

We report symmetry-breaking and restoring bifurcations of solitons in a fractional Schrodinger equation with cubic or cubic-quintic (CQ) nonlinearity and a parity-time-symmetric potential, which may be realized in optical cavities. Solitons are destabilized at the bifurcation point, and, in the case of CQ nonlinearity, the stability is restored by an inverse bifurcation. Two mutually conjugate branches of ghost states (GSs), with complex propagation constants, are created by the bifurcation, solely in the case of fractional diffraction. While GSs are not true solutions, direct simulations confirm that their shapes and results of their stability analysis provide a blueprint for the evolution of genuine localized modes in the system. (C) 2021 Optical Society of America

Automated summary

The study investigates symmetry-breaking and restoring bifurcations of solitons in a fractional Schrodinger equation, especially in the presence of CQ nonlinearity and a parity-time-symmetric potential. Solitons destabilize at the bifurcation point, but stability is restored through an inverse bifurcation in the case of CQ nonlinearity. Two mutually conjugate branches of ghost states are created in the presence of fractional diffraction.