Multifrequency and edge breathers in the discrete sine-Gordon system via subharmonic driving: theory, computation and experiment

TL;DR

This paper experimentally verifies the existence of multifrequency and edge breathers in a discrete sine-Gordon system driven subharmonically, confirming theoretical and numerical predictions through experiments and stability analysis.

Contribution

It provides the first experimental validation of multifrequency breathers and edge breathers in a driven discrete sine-Gordon system, aligning with recent theoretical and numerical studies.

Findings

Experimental confirmation of multifrequency breathers.

Observation of edge breathers localized at chain boundaries.

Good agreement between experiments, simulations, and analytical results.

Abstract

We consider a chain of torsionally-coupled, planar pendula shaken horizontally by an external sinusoidal driver. It has been known that in such a system, theoretically modeled by the discrete sine-Gordon equation, intrinsic localized modes, also known as discrete breathers, can exist. Recently, the existence of multifrequency breathers via subharmonic driving has been theoretically proposed and numerically illustrated by Xu {\em et al.} in Phys. Rev. E {\bf 90}, 042921 (2014). In this paper, we verify this prediction experimentally. Comparison of the experimental results to numerical simulations with realistic system parameters (including a Floquet stability analysis), and wherever possible to analytical results (e.g. for the subharmonic response of the single driven-damped pendulum), yields good agreement. Finally, we report on period-1 and multifrequency edge breathers which are localized at the open boundaries of the chain, for which we have again found good agreement between experiments and numerical computations