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Center for Nonlinear Studies |
We have simulated numerically the behavior of the one-dimensional, even, periodic alpha-FPU and Toda lattices to optical and acoustic excitations of varying amplitude. We have used the well-known diagnostics : localization parameter ; Lyapounov exponent , and slope of fit to linear normal mode energy. Space-time diagrams of local particle energy and a wave-related quantity are also shown. .The wave-related quantity, a discretization of the Riemann invariants of the alpha lattice, reveals soliton and near-soliton properties for acoustic excitations. In all alpha lattice cases, we have found signatures of approach to stochastic or chaotic behaviors at the same time. There is a clear separation in behaviors at long-time between integrable and nonintegrable systems.