• DOI:10.1063/1.2645141
• Corpus ID: 13226398

Tail resonances of Fermi-Pasta-Ulam q-breathers and their impact on the pathway to equipartition.

@article{Penati2007TailRO,
  title={Tail resonances of Fermi-Pasta-Ulam q-breathers and their impact on the pathway to equipartition.},
  author={Tiziano Penati and Sergej Flach},
  journal={Chaos},
  year={2007},
  volume={17 2},
  pages={
          023102
        }
}

• T. Penati, S. Flach
• Published 4 October 2006
• Physics
• Chaos

Upon initial excitation of a few normal modes the energy distribution among all modes of a nonlinear atomic chain (the Fermi-Pasta-Ulam model) exhibits exponential localization on large time scales. At the same time, resonant anomalies (peaks) are observed in its weakly excited tail for long times preceding equipartition. We observe a similar resonant tail structure also for exact time-periodic Lyapunov orbits, coined q-breathers due to their exponential localization in modal space. We give a simple explanation for this structure in terms of superharmonic resonances. The resonance analysis agrees very well with numerical results and has predictive power. We extend a previously developed perturbation method, based essentially on a Poincare-Lindstedt scheme, in order to account for these resonances, and in order to treat more general model cases, including truncated Toda potentials. Our results give a qualitative and semiquantitative account for the superharmonic resonances of q-breathers and natural packets.