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.