Scaling properties of q-breathers in nonlinear acoustic lattices

Recently q  -breathers—time-periodic solutions which localize in the space of normal modes and maximize the energy density for some mode vector q0q0—were obtained for finite nonlinear lattices. We scale these solutions together with the size of the system to arbitrarily large lattices. The first finding is that the degree of localization depends only on intensive quantities and is size independent. Secondly a critical wave vector kmkm is identified, which depends on one effective nonlinearity parameter. q  -breathers minimize the localization length at k0=kmk0=km and completely delocalize in the limit k0→0k0→0.