Scaling properties of $q$-breathers in nonlinear acoustic lattices

Abstract

Recently $q$-breathers - time-periodic solutions which localize in the space of normal modes and maximize the energy density for some mode vector $q_0$ - were obtained for finite nonlinear lattices. We scale these solutions together with the size of the system to arbitrarily large lattices. We generalize previously obtained analytical estimates of the localization length of $q$-breathers. The first finding is that the degree of localization depends only on intensive quantities and is size independent. Secondly a critical wave vector $k_m$ is identified, which depends on one effective nonlinearity parameter. $q$-breathers minimize the localization length at $k_0=k_m$ and completely delocalize in the limit $k_0\to 0$.

4 pages, 5 figures

References in corpus (1)

• q-breathers in finite two- and three-dimensional nonlinear acoustic lattices

Cited by in corpus (6)

• The Fermi-Pasta-Ulam problem: periodic orbits, normal forms and resonance overlap criteria
• Tail resonances of FPU q-breathers and their impact on the pathway to equipartition
• Boundary effects on quantum q-breathers in a Bose-Hubbard chain
• Periodic orbits, localization in normal mode space, and the Fermi-Pasta-Ulam problem
• q-breathers in Discrete Nonlinear Schroedinger lattices
• Extensive packet excitations in FPU and Toda lattices