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