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math.AP2026
The Fermi-Pasta-Ulam system and the Korteweg-de Vries equation: a low-regularity continuum limit
Herbert Koch, Ruoyuan Liu
For the infinite Fermi-Pasta-Ulam (FPU) system, general solutions can be approximated by counter-propagating waves associated with solutions to the Korteweg-de Vries (KdV) equation…
nlin.SI2026
The Korteweg-de Vries limit for the global dynamics of the Toda lattice
Ruoyuan Liu, Herbert Koch
It has been observed that the dynamics of the Toda lattice can be well described by solutions of the Korteweg-de Vries (KdV) equation in the continuum limit. We show that, under th…