Stability, integrability, and nonlinear dynamics of PT-symmetric optical couplers with cubic cross-interactions or cubic-quintic nonlinearities

We explore the parity-time-( PT)-symmetric optical couplers with the cubic both self- and cross-interactions corresponding to self- and cross-phase modulations. When the coefficient of the cubic cross-interaction is chosen as the different values, we find three distinct cases for two branches, including the stable-stable modes (linear unbroken PT-symmetric phase), stable-unstable modes (linear unbroken PT-symmetric phase), as well as unstable-unstable modes (linear broken PT-symmetric phase). Moreover, we find the periodic trajectories for some parameters. Similarly, we also explore the PT-symmetric optical couplers with cubic-quintic self-phase modulations. We numerically give the stable and unstable regions of the cubic-quintic system. Moreover, we also find the periodic trajectories for some parameters in the Stokes domain.