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

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

7 pages, 8 figures

References in corpus (5)

• Observation of surface gap solitons in semi-infinite waveguide arrays
• Observation of two-dimensional surface solitons in anisotropic waveguide arrays
• Driven Intrinsic Localized Modes in a Coupled Pendulum Array
• Peierls-Nabarro Barrier and Protein Loop Propagation
• Instability dynamics and breather formation in a horizontally shaken pendulum chain

Cited by in corpus (4)

• Experimental and numerical observation of dark and bright discrete solitons in the band-gap of a diatomic-like electrical lattice
• Stabilization of the coupled pendula chain under parametric PT-symmetric driving force
• Patterns and Stability of Coupled Multi-Stable Nonlinear Oscillators
• Nonlinear edge modes in a honeycomb electrical lattice near the Dirac points