Experimental Results for the sine-Gordon Equation in Arrays of Coupled Torsion Pendula

Abstract

The pendulum chain with torsional spring coupling represents a physical system that is described exactly by the spatially discrete sG equation. In order to study its solutions experimentally, however, we have to drive the system to counteract the inevitable dissipation we face in experiments. In fact, it is important to model the main sources of energy dissipation realistically; here we find that both on-site and intersite contributions to dissipation are relevant. We show that lattice solitons, also known as discrete breathers (DB) or intrinsic localized modes (ILMs), can be produced and stabilized in this system in the presence of driving (forcing) and damping. One way to do this is by exploiting the modulational instability of the uniform mode. Once a discrete soliton has been phase-locked to the driver, it persists indefinitely, and its properties can be studied, as can the range of its stability in parameter space and the types of instability outside of it. We also explore in some detail the interesting effect of which there exists no analogue in continuous media: the existence of two types of discrete solitons of different symmetry—the one-site centered and the two-site centered ILM. Furthermore, we find an exchange of stability between those two breather types as certain system parameters are varied. Comparison to analytical work based on realistic model parameters will be discussed as well.