title: Korteweg-de Vries equation and energy sharing in Fermi-Pasta-Ulam.
abstract: We address the problem of equipartition in a long Fermi-Pasta-Ulam (FPU) chain. After giving a precise relation between FPU and Korteweg-de Vries we use the latter equation to show that, corresponding to initial data a la Fermi, the time average of the energy on the kth mode decreases exponentially with kN. The result persists in the thermodynamic limit.
authors.affiliation: Università degli Studi di Milano, Dipartimento di Matematica F. Enriques, Via Saldini 50, 20133 Milan, Italy. ponno@mat.unimi.it
authors.forename: A
authors.initials: A
authors.lastname: Ponno
authors.forename: D
authors.initials: D
authors.lastname: Bambusi