Long-time Korteweg-de Vries approximation for the Fermi-Pasta-Ulam-Tsingou system

Younghun Hong; Junyeong Jang

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arXiv · 2609.30668

Long-time Korteweg-de Vries approximation for the Fermi-Pasta-Ulam-Tsingou system

Younghun Hong·Junyeong Jang

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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 $L^2$ 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.

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Younghun Hong, Junyeong Jang. 2026-09-25. Long-time Korteweg-de Vries approximation for the Fermi-Pasta-Ulam-Tsingou system. https://arxiv.org/abs/2609.30668

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