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 k/N. The result persists in the thermodynamic limit.
Korteweg-de Vries equation and energy sharing in Fermi-Pasta-Ulam
PONNO, ANTONIO;
2005
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 k/N. The result persists in the thermodynamic limit.
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