- 05-218 D. Bambusi, A. Ponno
- On Metastability in FPU
(361K, pdf)
Jun 20, 05
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Abstract. We present an analytical study of the Fermi--Pasta--Ulam (FPU)
$\alpha$--model with periodic boundary conditions. We analyze the
dynamics corresponding to initial data with some low frequency Fourier
modes excited. We show that, correspondignly, a pair of KdV equations
constitute the resonant normal form of the system. We also use such a
normal form in order to prove the existence of a metastability
phenomenon. More precisely, we show that the time average of the modal
energy spectrum rapidly attains a well defined distribution
corresponding to a packet of low frequencies modes. Subsequently, the
distribution remains unchanged up to the time scales of validity of
our approximation. The phenomenon is controlled by the specific
energy.
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