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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