V Koukouloyannis, PG Kevrekidis, J Cuevas and V Rothos (pdf copy 744 Kb.)
We study the existence and stability of multibreathers in Klein–Gordon chains with interactions that are not restricted to nearest neighbors. We provide a general framework where such long range effects can be taken into consideration for arbitrarily varying (as a function of the node distance) linear couplings between arbitrary sets of neighbors in the chain. By examining special case examples such as three-site breathers with next-nearest-neighbors, we find crucial modifications to the nearest-neighbor picture of one-dimensional oscillators being excited either in- or anti-phase. Configurations with nontrivial phase profiles emerge from or collide with the ones with standard (0 or π) phase difference profiles, through supercritical or subcritical bifurcations respectively. Similar bifurcations emerge when examining foursite breathers with either next-nearest-neighbor or even interactions with the three-nearest onedimensional neighbors. The latter setting can be thought of as a prototype for the two-dimensional building block, namely a square of lattice nodes, which is also examined.
Physica D 242 (2013) 16-29
doi: 10.1016/j.physd.2012.08.011