Korteweg–de Vries equation and energy sharing in Fermi–Pasta–Ulam
- 1 March 2005
- journal article
- Published by AIP Publishing in Chaos: An Interdisciplinary Journal of Nonlinear Science
- Vol. 15 (1) , 15107
- https://doi.org/10.1063/1.1832772
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 à la Fermi, the time average of the energy on the kth mode decreases exponentially with k∕N. The result persists in the thermodynamic limit.Keywords
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