Korteweg-de Vries equation and energy sharing in Fermi-Pasta-Ulam.
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.
Ponno
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Università degli Studi di Milano, Dipartimento di Matematica F. Enriques, Via Saldini 50, 20133 Milan, Italy. ponno@mat.unimi.it
Bambusi
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