00-133 PONNO A.,GALGANI L., GUERRA F.
An analytical estimate of stochasticity thresholds in Fermi-Pasta-Ulam and $\phi^4$ models. (327K, PostScript) Mar 29, 00
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Abstract. We consider an infinitely extended FPU model, and we show that the slow modulating amplitude of a narrow wave packet asymptotically satisfies the Nonlinear Schrodinger equation (NLS). It is well known that NLS presents a threshold below which the packet width remains narrow. We give an analytical estimate of such a threshold; we also make a comparison with the numerical results known to us, and show they are in remarkable agreement with our estimate. Analogous results are found for the $\phi^4$ model.

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