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Long-time Korteweg-de Vries approximation for the Fermi-Pasta-Ulam-Tsingou system
Abstract
We prove that, as the lattice spacing h tends to zero, general solutions to the infinite Fermi--Pasta--Ulam--Tsingou (FPUT) system can be approximated in L2 by two counter-propagating Korteweg--de Vries (KdV) waves on time intervals of order log(1/h). This resolves an open question raised by the first author and collaborators~\cite{HKY2021}. Our proof combines the FPUT conservation law with an h-uniform local well-posedness theory in L2 and persistence of Sobolev regularity. We also introduce a frequency-localized auxiliary equation to overcome the difficulty of comparing the Fourier restriction norms associated with the FPUT and KdV flows.
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BibTeX
@misc{hong2026longtime,
title = {{Long-time Korteweg-de Vries approximation for the Fermi-Pasta-Ulam-Tsingou system}},
author = {Younghun Hong and Junyeong Jang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.30668},
eprint = {2609.30668},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30668},
}
RIS
TY - UNPB
TI - Long-time Korteweg-de Vries approximation for the Fermi-Pasta-Ulam-Tsingou system
AU - Younghun Hong
AU - Junyeong Jang
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2609.30668
UR - https://arxiv.org/abs/2609.30668
AB - We prove that, as the lattice spacing h tends to zero, general solutions to the infinite Fermi--Pasta--Ulam--Tsingou (FPUT) system can be approximated in L^2 by two counter-propagating Korteweg--de Vries (KdV) waves on time intervals of order log(1/h). This resolves an open question raised by the first author and collaborators~\cite{HKY2021}. Our proof combines the FPUT conservation law with an h-uniform local well-posedness theory in L^2 and persistence of Sobolev regularity. We also introduce a frequency-localized auxiliary equation to overcome the difficulty of comparing the Fourier restriction norms associated with the FPUT and KdV flows.
ER -