Resonant localized modes in electrical lattices with second-neighbor coupling

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 plane-wave mode of the same frequency. This kind of localized mode has also been termed a 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 wave number $k=0$), we observed stable ILMs as well as a periodic localization pattern in certain driving regimes. In the zone boundary case (of wave number $k=\ensuremath{\pi}/a$, where $a$ is the lattice spacing), the ILMs are always resonant with a plane-wave mode, but they can nevertheless be stabilized by direct (staggered) and subharmonic driving.