PreprintCC BY 4.0arXiv
Long time stability of low--frequency packets of modes at finite total energy
Abstract
We consider the FPUT α-model with N particles and initial data with small total energy E, independent of N. In particular, we prove that if the energy is initially given to Fourier modes of wave number πk/N≤ θ*, then it does not flow to modes of wave number larger than θ* up to long times of order E−(1−ε/2), θ* and ε being small numbers. The proof relies on the closeness of the Toda lattice to the FPUT system. Unlike previous approaches, we do not make use of the action-angle variables of the Toda system, but we exploit the Flaschka integrals of the latter. Actually, we find a suitable recombination of the Flaschka integrals whose quadratic part is used to control the packet, the higher order part fulfilling very good estimates.
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BibTeX
@misc{bambusi2026long,
title = {{Long time stability of low--frequency packets of modes at finite total energy}},
author = {Dario Bambusi and Antonio Ponno},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.23119},
eprint = {2609.23119},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.23119},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Long time stability of low--frequency packets of modes at finite total energy
AU - Dario Bambusi
AU - Antonio Ponno
PY - 2026
DA - 2026/09/19
PB - arXiv
DO - 10.48550/arxiv.2609.23119
UR - https://arxiv.org/abs/2609.23119
AB - We consider the FPUT α-model with N particles and initial data with small total energy E, independent of N. In particular, we prove that if the energy is initially given to Fourier modes of wave number πk/N≤ θ_*, then it does not flow to modes of wave number larger than θ_* up to long times of order E^−(1−ε/2), θ_* and ε being small numbers. The proof relies on the closeness of the Toda lattice to the FPUT system. Unlike previous approaches, we do not make use of the action-angle variables of the Toda system, but we exploit the Flaschka integrals of the latter. Actually, we find a suitable recombination of the Flaschka integrals whose quadratic part is used to control the packet, the higher order part fulfilling very good estimates.
ER -