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q-Breathers and the Fermi-Pasta-Ulam Problem M. V. Ivanchenko,2

Summary: q-Breathers and the Fermi-Pasta-Ulam Problem
S. Flach,1
M. V. Ivanchenko,2
and O. I. Kanakov2
Max-Planck-Institut fu¨r Physik komplexer Systeme, No¨thnitzer Strasse 38, D-01187 Dresden, Germany
Department of Radiophysics, Nizhny Novgorod University, Gagarin Avenue, 23, 603950 Nizhny Novgorod, Russia
(Received 15 April 2005; published 2 August 2005)
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 q. We continue normal modes from
the harmonic limit into the FPU parameter regime and obtain persistence of these periodic orbits, termed
here q-breathers (QB). They are characterized by time periodicity, exponential localization in the q-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.
DOI: 10.1103/PhysRevLett.95.064102 PACS numbers: 63.20.Pw, 05.45.2a, 63.20.Ry
Fifty years ago Fermi, Pasta, and Ulam (FPU) published
their celebrated paper on thermalization of arrays of parti-


Source: Aickelin, Uwe - School of Computer Science, University of Nottingham
Flach, Sergej - Max-Planck-Institut für Physik komplexer Systeme


Collections: Computer Technologies and Information Sciences; Physics