q-Breathers in Fermi-Pasta-Ulam chains: existence, localization and stability
S. Flach, M. V. Ivanchenko, O. I. Kanakov
Abstract
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.
Create a lesson
Related papers
Synchronization transitions in ensembles of active particles with distance-dependent higher-order interactions
Dhrubajyoti Biswas, P. S. Burada, Pintu Patra
Effect of high odrer dispersion on soliton interaction in coupled Kerr cavities
Andrei G. Vladimirov
Aberration stabilized light bullets in normal dispersion injected Kerr resonators
Yannick Fleck, Thomas G. Seidel, Jesús Yelo-Sarrión et al.
Rate-selective synchronization in switching networks: when timing meets structure
Russell Jeter, Angelo Boateng, Maurizio Porfiri et al.
On the Time-Domain Waveforms Leading to Frequency Comb Spectra
Madhurendra Mishra, Adarsh Ganesan
Oscillatory instability of subcritical stationary solutions in the parametrically driven, damped nonlinear Dirac equation
Fernando Carreño-Navas