Breathers in Hamiltonian ${\cal PT}$-symmetric chains of coupled pendula   under a resonant periodic force
  We derive a Hamiltonian version of the ${\cal PT}$-symmetric discrete nonlinear Schr\"{o}dinger 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. 
Alexander Chernyavsky and Dmitry E. Pelinovsky
math-ph math.DS math.MP nlin.PS