Nonlinear localized modes in the classical XY model

Abstract

It is shown that rotobreathers are generic solutions of the two-dimensional XY model with the nearest-neighbour interactions. Rotobreathers are periodic and spatially localized modes that cosist of several sites that rotate with some given frequency ω, while the rest of the lattice oscillates with the same frequency. The allowed range of the rotobreather frequencies begins from the upper edge of the linear spectrum Ω_π and continues to the arbitrarily large frequencies. Rotobreathers are linearly stable for the frequencies ω that satisfty the ineaquality ω > 2Ω_π