Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Hong, Younghun, Jang, Junyeong
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214595956