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

TL;DR

This paper derives a Hamiltonian ${ m PT}$-symmetric model for coupled pendula under periodic forcing, classifies breather solutions, and analyzes their stability, advancing understanding of localized oscillations in nonlinear lattice systems.

Contribution

It introduces a Hamiltonian ${ m PT}$-symmetric discrete nonlinear Schrödinger equation for coupled pendula and analyzes breather existence and stability in this framework.

Findings

Breathers exist near a pair of coupled pendula.

Spectral stability of breathers is characterized.

Orbital stability is established in certain parameter regions.

Abstract

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.