-Breathers and the Fermi-Pasta-Ulam Problem
Phys. Rev. Lett. 95, 064102 – Published 2 August, 2005
DOI: https://doi.org/10.1103/PhysRevLett.95.064102
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.