Integrability and trajectory confinement in -symmetric waveguide arrays

We consider $\mathcal{PT}$-symmetric ring-like arrays of optical waveguides with purely nonlinear gain and loss. Regardless the value gain-loss coefficient, these systems are protected from spontaneous $\mathcal{PT}$-symmetry breaking. If nonhermitian part array matrix has cross-compensating structure, total power in such a system remains bounded -- or even constant at all times. identify two-, three-, four-waveguide cross-compensatory loss that constitute completely integrable Hamiltonian systems.