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q-breathers in Fermi-Pasta-Ulam chains: Existence, localization, and stability M. V. Ivanchenko,2
 

Summary: q-breathers in Fermi-Pasta-Ulam chains: Existence, localization, and stability
S. Flach,1
M. V. Ivanchenko,2
and O. I. Kanakov2
1
Max-Planck-Institut für Physik Komplexer Systeme, Nöthnitzer Strasse 38, D-01187 Dresden, Germany
2
Department of Radiophysics, Nizhny Novgorod University, Gagarin Avenue, 23, 603950 Nizhny Novgorod, Russia
Received 30 August 2005; published 24 March 2006
The Fermi-Pasta-Ulam FPU problem 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/PhysRevE.73.036618 PACS number s : 05.45. a, 63.20.Pw, 63.20.Ry
I. INTRODUCTION
In 1955, Fermi, Pasta, and Ulam FPU published their

  

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