The Fermi-Pasta-Ulam problem. A status report
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Publication:2474328
DOI10.1007/978-3-540-72995-2zbMath1138.81004OpenAlexW80779078MaRDI QIDQ2474328
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Publication date: 5 March 2008
Published in: Lecture Notes in Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/978-3-540-72995-2
Collections of articles of miscellaneous specific interest (00B15) Proceedings, conferences, collections, etc. pertaining to quantum theory (81-06) Molecular physics (81V55) Proceedings, conferences, collections, etc. pertaining to statistical mechanics (82-06)
Related Items (73)
NONLINEAR WAVES IN NEWTON'S CRADLE AND THE DISCRETE p-SCHRÖDINGER EQUATION ⋮ The Fermi-Pasta-Ulam problem: scaling laws vs. initial conditions ⋮ On the periodic orbits of four-particle time-dependent FPU chains ⋮ Solitary waves in FPU-type lattices ⋮ Packets of resonant modes in the Fermi-Pasta-Ulam system ⋮ Traveling waves for the mass in mass model of granular chains ⋮ Thermalization without chaos in harmonic systems ⋮ On typicality in nonequilibrium steady states ⋮ Fermi-Pasta-Ulam-Tsingou problems: passage from Boltzmann to \(q\)-statistics ⋮ An energy-based stability criterion for solitary travelling waves in Hamiltonian lattices ⋮ Energy separation in oscillatory Hamiltonian systems without any non-resonance condition ⋮ Understanding the FPU state in FPU-like models ⋮ Elliptic tori in FPU non-linear chains with a small number of nodes ⋮ Normal form for lower dimensional elliptic tori in Hamiltonian systems ⋮ Periodic travelling waves and compactons in granular chains ⋮ Travelling waves in nonlinear magneto-inductive lattices ⋮ Wave turbulence and thermalization in one-dimensional chains ⋮ Solitary wave propagation in a two-dimensional lattice ⋮ Thermalization of a driven bi-stable FPU chain ⋮ The effect of loss/gain and Hamiltonian perturbations of the Ablowitz—Ladik lattice on the recurrence of periodic anomalous waves ⋮ Energy exchange and transition to localization in the asymmetric Fermi-pasta-Ulam oscillatory chain ⋮ Modulation instability, periodic anomalous wave recurrence, and blow up in the Ablowitz–Ladik lattices ⋮ Wave propagation in one-dimensional nonlinear acoustic metamaterials ⋮ Emergence of rogue waves from optical turbulence ⋮ On the role of the integrable Toda model in one-dimensional molecular dynamics ⋮ Dynamical systems on lattices with decaying interaction. I: A functional analysis framework ⋮ Fermi-Pasta-Ulam chains with harmonic and anharmonic long-range interactions ⋮ Time-scales to equipartition in the Fermi-Pasta-Ulam problem: finite-size effects and thermodynamic limit ⋮ Traveling solitons in long-range oscillator chains ⋮ Localized stable manifolds for whiskered tori in coupled map lattices with decaying interaction ⋮ Dynamical phase transition in the simplest molecular chain model ⋮ On intense energy exchange and localization in periodic FPU dimer chains ⋮ Behavior and breakdown of higher-order Fermi-Pasta-Ulam-Tsingou recurrences ⋮ Strong and weak chaos in weakly nonintegrable many-body Hamiltonian systems ⋮ Existence of solitary traveling waves in a system of nonlinearly coupled oscillators on the 2D lattice ⋮ Energy spreading in strongly nonlinear disordered lattices ⋮ Memory effects in the Fermi-Pasta-Ulam model ⋮ On the Behavior of the Generalized Alignment Index (GALI) Method for Regular Motion in Multidimensional Hamiltonian Systems ⋮ Law without law or ``just limit theorems? Some reflections about a proposal of Wheeler's ⋮ Long range correlations in stochastic transport with energy and momentum conservation ⋮ Equilibration properties of classical integrable field theories ⋮ Pulse solutions of the fractional effective models of the Fermi–Pasta–Ulam lattice with long-range interactions ⋮ The FPU problem as a statistical-mechanical counterpart of the KAM problem, and its relevance for the foundations of physics ⋮ Discrete rational and breather solution in the spatial discrete complex modified Korteweg-de Vries equation and continuous counterparts ⋮ Nonlinear fluctuating hydrodynamics for anharmonic chains ⋮ An averaging theorem for FPU in the thermodynamic limit ⋮ Freezing of the optical-branch energy in a diatomic FPU chain ⋮ Some breathers and multi-breathers for FPU-type chains ⋮ Equilibrium thermodynamics and thermodynamic processes in nonlinear systems ⋮ On the Korteweg-de Vries limit for the Fermi-Pasta-Ulam system ⋮ On the energy distribution in Fermi-Pasta-Ulam lattices ⋮ Statistical distribution of bonding distances in a unidimensional solid ⋮ The Fermi-pasta-Ulam problem and its underlying integrable dynamics: an approach through Lyapunov exponents ⋮ Metastable Energy Strata in Weakly Nonlinear Wave Equations ⋮ Statistical mechanics of an integrable system ⋮ Solitary waves on nonlocal Fermi-Pasta-Ulam lattices: exponential localization ⋮ The finite-gap method and the periodic NLS Cauchy problem of anomalous waves for a finite number of unstable modes ⋮ K for KAM. Kolmogorov-Arnold-Moser. Translated from the Italian ⋮ Stages of dynamics in the Fermi-Pasta-Ulam system as probed by the first Toda integral ⋮ Breathers and other time-periodic solutions in an array of cantilevers decorated with magnets ⋮ Universal route to thermalization in weakly-nonlinear one-dimensional chains ⋮ Horseshoes for Singly Thermostated Hamiltonians ⋮ Supersonic kinks and solitons in active solids ⋮ Justification of the KP-II approximation in dynamics of two-dimensional FPU systems ⋮ An extensive adiabatic invariant for the Klein-Gordon model in the thermodynamic limit ⋮ The linear and nonlinear instability of the Akhmediev breather ⋮ Dynamics of periodic Toda chains with a large number of particles ⋮ Ergodicity: How Can It Be Broken? ⋮ Dispersive shock waves in lattices: a dimension reduction approach ⋮ Nekhoroshev theorem for the periodic Toda lattice ⋮ Construction of invariant whiskered tori by a parameterization method. II: Quasi-periodic and almost periodic breathers in coupled map lattices ⋮ Thermalization of isolated harmonic networks under conservative noise ⋮ Quantum superexponential oscillator
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