q-Breathers and the Fermi-Pasta-Ulam Problem
Abstract
The Fermi-Pasta-Ulam (FPU) paradox consists of the nonequipartition of energy among normal modes of a weakly anharmonic atomic chain model. In the harmonic limit each normal mode corresponds to a periodic orbit in phase space and is characterized by its wave number . We continue normal modes from the harmonic limit into the FPU parameter regime and obtain persistence of these periodic orbits, termed here -Breathers (QB). They are characterized by time periodicity, exponential localization in the -space of normal modes and linear stability up to a size-dependent threshold amplitude. Trajectories computed in the original FPU setting are perturbations around these exact QB solutions. The QB concept is applicable to other nonlinear lattices as well.
Keywords
Cite
@article{arxiv.nlin/0504036,
title = {q-Breathers and the Fermi-Pasta-Ulam Problem},
author = {S. Flach and M. V. Ivanchenko and O. I. Kanakov},
journal= {arXiv preprint arXiv:nlin/0504036},
year = {2009}
}
Comments
4 pages, 4 figures