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 $k_0\to 0$.

arXiv comment4 pages, 5 figures

References in corpus (5)

• q-Breathers and the Fermi-Pasta-Ulam Problem
• q-Breathers in Fermi-Pasta-Ulam chains: existence, localization and stability
• Bushes of vibrational modes for Fermi-Pasta-Ulam chains
• Symmetric invariant manifolds in the Fermi-Pasta-Ulam lattice
• q-breathers in finite two- and three-dimensional nonlinear acoustic lattices

Cited by in corpus (10)

• Energy localization on q-tori, long term stability and the interpretation of FPU recurrences
• 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
• Discrete Symmetry and Stability in Hamiltonian Dynamics
• Low-dimensional q-Tori in FPU Lattices: Dynamics and Localization Properties
• Periodic orbits, localization in normal mode space, and the Fermi-Pasta-Ulam problem
• Boundary effects on quantum q-breathers in a Bose-Hubbard chain
• $q$-Breathers in finite lattices: nonlinearity and weak disorder
• q-breathers in Discrete Nonlinear Schroedinger lattices
• Extensive packet excitations in FPU and Toda lattices