We study a long-range–interaction generalisation of the one-dimensional Fermi-PastaUlam (FPU) β-model, by introducing a quartic interaction coupling constant that decays as 1/r (α ≥ 0) (with strength characterised by b > 0). In the α → ∞ limit we recover the original FPU model. Through molecular dynamics we show that i) for α ≥ 1 the maximal Lyapunov exponent remains finite and positive for an ...

In recent y ears computer applications have increased in their computational complexity. The industry-wide usage of performance benchmarks, such as SPECmarks, forces processor designers to pay particular attention to implementation of the oating point unit, or FPU. Special purpose applications, such as high performance graphics rendering systems, have placed further demands on processors. High ...

In this paper we construct a higher order expansion of the manifold quasi unidirectional waves in Fermi-Pasta-Ulam (FPU) chain. We also approximate dynamics on manifold. As perturbation parameter use $h^2=1/n^2$, where $n$ is number particles It well known that described to first by Korteweg-de Vries (KdV) equation. Here show second governed combination two nontrivial equations KdV hierarchy --...

We show the relevance of the dispersive analogue of the shock waves in the FPU dynamics. In particular we give strict numerical evidences that metastable states emerging from low frequency initial excitations, are indeed constituted by dispersive shock waves travelling through the chain. Relevant characteristics of the metastable states, such as their frequency extension and their time scale of...

2 Some Equations of Interest 2 2.1 FPU and DNLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 The Davydov System, and Some Reductions . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.3 Invariants (a.k.a Conserved Quantities, First Integrals) . . . . . . . . . . . . . . . . . . . . . 7 2.4 More General Lattice Equations . . . . . . . . . . . . . ....

We revisit an algorithm constructing elliptic tori, that was originally designed for applications to planetary hamiltonian systems. The scheme is adapted properly work with models of chains $N+1$ particles interacting via anharmonic potentials, thus covering also the case FPU chains. After having preliminarily settled Hamiltonian in a suitable way, we perform sequence canonical transformations ...