The Fermi-Pasta-Ulam problem and the Korteweg - de Vries equation


Lunedi' 13 ottobre alle ore 11 in aula 2AB/45 Antonio Ponno (Dipartimento di Matematica P.A.) terra' un seminario dal titolo "The Fermi-Pasta-Ulam problem and the Korteweg - de Vries equation".

A short introduction to the classical Fermi-Pasta-Ulam (FPU) problem is given. In particular, some relevant scaling laws underlying the dynamics and the phenomenology of the latter are both explained in terms of the Korteweg - de Vries (KdV) equation and of the regularity properties of its solutions. More precisely, the resonant normal form equations of the FPU problem with N degrees of freedom and fixed ends are shown to coincide with the Fourier-Galerkin truncation to N modes of a suitable KdV equation on the unit circle. This is the precise technical ingredient allowing for the explanation of many features of the FPU phenomenology over short time-scales in terms of the KdV equation, which is an integrable PDE.

Rif. int M. Bardi, P. Mannucci, A. Cesaroni

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