Integrability and trajectory confinement in -symmetric waveguide arrays

Abstract

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