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

• We have confirmed experimentally the existence of subharmonic ILM/breather structures in a chain of coupled torsion pendula.
• Experiments are in line with our theoretical analysis and numerical computations.
• We have also revealed surface breather modes in this chain, both experimentally and numerically.

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 et al. (2014) [21]. 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 the 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.