Resonant Localized Modes in Electrical Lattices with Second Neighbor Coupling

TL;DR

This study explores how electrical lattices with second-neighbor coupling can support both standard and resonant localized modes, demonstrating experimental and numerical stabilization methods for these complex structures.

Contribution

It introduces the experimental and numerical demonstration of stable resonant ILMs, or nanopterons, in electrical lattices with second-neighbor coupling, including stabilization techniques.

Findings

Stable ILMs observed at zone center and boundary.

Resonant ILMs (nanopterons) can be stabilized via driving.

Resonant ILMs exhibit oscillations due to mode resonance.

Abstract

We demonstrate experimentally and corroborate numerically that an electrical lattice with nearest-neighbor and second-neighbor coupling can simultaneously support long-lived coherent structures in the form of both standard intrinsic localized modes (ILMs), as well as resonant ILMs. In the latter case, the wings of the ILM exhibit oscillations due to resonance with a degenerate plane-wave mode. This kind of localized mode has also been termed nanopteron. Here we show experimentally and using realistic simulations of the system that the nanopteron can be stabilized via both direct and subharmonic driving. In the case of excitations at the zone center (i.e., at wavenumber $k=0$), we observed stable ILMs, as well as a periodic localization pattern in certain driving regimes. In the zone boundary case (of wavenumber $k=\pi/a$, where $a$ is the lattice spacing), the ILMs are always resonant with a plane-wave mode, but can nevertheless be stabilized by direct (staggered) and subharmonic driving.