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

2016/05/20 by Chernyavsky, Alexander, Pelinovsky, Dmitry E.
#Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Pattern Formation and Solitons (nlin.PS)

paper · doi:10.48550/arxiv.1605.06455

Abstract

We derive a Hamiltonian version of the \cal 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.

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