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On Metastability in FPU
We present an analytical study of the Fermi–Pasta–Ulam (FPU) α–model with periodic boundary conditions. We analyze the dynamics corresponding to initial data with one low frequency Fourier mode… Expand
Time-Scales to Equipartition in the Fermi–Pasta–Ulam Problem: Finite-Size Effects and Thermodynamic Limit
We investigate numerically the common α+β and the pure β FPU models, as well as some higher order generalizations. We consider initial conditions in which only low-frequency normal modes are excited,… Expand
Korteweg-de Vries equation and energy sharing in Fermi-Pasta-Ulam.
We address the problem of equipartition in a long Fermi-Pasta-Ulam (FPU) chain. After giving a precise relation between FPU and Korteweg-de Vries we use the latter equation to show that,… Expand
The nonlinear Schrödinger equation as a resonant normal form
Averaging theory is used to study the dynamics of dispersive equations taking the nonlinear Klein Gordon equation on the line as a model problem: For approximatively monochromatic initial data of… Expand
The Fermi–Pasta–Ulam problem: Periodic orbits, normal forms and resonance overlap criteria
Abstract Fermi, Pasta and Ulam observed that the excitation of a low frequency normal mode in a nonlinear acoustic chain leads to localization in normal mode space on large time scales. Fast… Expand
The Fermi–Pasta–Ulam Problem and Its Underlying Integrable Dynamics: An Approach Through Lyapunov Exponents
FPU models, in dimension one, are perturbations either of the linear model or of the Toda model; perturbations of the linear model include the usual $$\beta $$β-model, perturbations of Toda include… Expand
The Fermi-Pasta-Ulam Problem and Its Underlying Integrable Dynamics
This paper is devoted to a numerical study of the familiar α+β FPU model. Precisely, we here discuss, revisit and combine together two main ideas on the subject: (i) In the system, at small specific… Expand
Energy localization in the Peyrard-Bishop DNA model.
- J. De Luca, E. Drigo Filho, A. Ponno, J. R. Ruggiero
- Mathematics, Medicine
- Physical review. E, Statistical, nonlinear, and…
- 14 May 2004
We study energy localization on the oscillator chain proposed by Peyrard and Bishop to model DNA. We search numerically for conditions with initial energy in a small subgroup of consecutive… Expand
The two-stage dynamics in the Fermi-Pasta-Ulam problem: from regular to diffusive behavior.
A numerical and analytical study of the relaxation to equilibrium of both the Fermi-Pasta-Ulam (FPU) α-model and the integrable Toda model, when the fundamental mode is initially excited, is… Expand
Soliton theory and the Fermi-Pasta-Ulam problem in the thermodynamic limit
- A. Ponno
- 1 December 2003
We reconsider the Fermi-Pasta-Ulam problem from the point of view of soliton theory along the lines of the original work of Zabusky and Kruskal, but with attention to the thermodynamic limit. For a… Expand