The role of integrability in Fermi-Pasta-Ulam-Tsingou-like models

Abstract

In these lecture notes, we present, contextualize, and discuss the phenomenon of metastability (or prethermalization) in the Fermi-Pasta-Ulam-Tsingou lattice and similar models from the viewpoint of perturbation theory. We provide an updated state-of-the-art description of this intermediate state in terms of the underlying integrable dynamics, in particular the Korteweg-de Vries and inviscid Burgers equations.

Lecture notes for a course at ASIDE summmer school -- Summer 2025. Version accepted for publication on the volume "Symmetries and Integrability of Difference Equations". Last version: corrected some typos