Symmetry breaking and dynamics of solitons in regular and parity-time-symmetric nonlinear coupler supported by fractional dispersion

The present work investigates symmetry breaking in dual-core couplers with fractional dispersion, cubic self-focusing, gain and loss effects acting in each core, modeled by coupled fractional nonlinear Schrödinger equations with Lévy index. We demonstrate that spontaneous symmetry breaking (SSB) bifurcations of solitons in the regular and parity-time (PT) symmetric fractional coupler with fractional dispersion and cubic nonlinearity. Two types of the asymmetric solutions emerge by way of symmetry breaking bifurcations. By dint of numerical calculations, we identify the symmetry breaking phase transitions of both the first and second kinds (alias sub- and supercritical bifurcations) for symmetric and antisymmetric solitons in the regular fractional couplers. For PT-symmetric fractional nonlinear coupler, the branches of asymmetry solutions are existing with complex conjugate propagation constants (alias ghost states). Moreover, we investigate the dependence of Lévy index on the symmetry breaking of solitons in detail. The stabilities and evolution of the solitons and asymmetric solutions are explored.