A. Chernyavsky and D.E. Pelinovsky

Breathers in Hamiltonian PT-symmetric chains of coupled pendula under a resonant periodic force

Symmetry 8 (2016), 59 (26 pages)

We derive a Hamiltonian version of the PT-symmetric discrete nonlinear Schršodinger 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.

PT-symmetry, discrete nonlinear Schrodinger equation, Hamiltonian structure, discrete breathers, existence and stability.