Breathers in Hamiltonian PT -Symmetric Chains of Coupled Pendula under a Resonant Periodic Force

We derive a Hamiltonian version of the PT -symmetric discrete nonlinear Schrödinger equation that describes synchronized dynamics of coupled pendula driven by a periodic movement of their common strings. In the limit of weak coupling between the pendula, we classify the existence and spectral stability of breathers (time-periodic solutions localized in the lattice) supported near one pair of coupled pendula. Orbital stability or instability of breathers is proved in a subset of the existence region