Proof of Nishida's conjecture on anharmonic lattices

DOI10.1007/s00220-005-1451-1zbMath1113.82045arXivnlin/0506024OpenAlexW2143285310WikidataQ123287155 ScholiaQ123287155MaRDI QIDQ852362

Bob Rink

Publication date: 29 November 2006

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/nlin/0506024

zbMATH Keywords

Fermi-Pasta-Ulam latticeKolmogorov-Arnold-Moser (KLM) theoremNishida's conjecture

Mathematics Subject Classification ID

Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics (82C20) Lattice dynamics; integrable lattice equations (37K60)

Related Items

Cnoidal waves on Fermi-Pasta-Ulam lattices ⋮ Resonant normal form for even periodic FPU chains ⋮ Wave turbulence and thermalization in one-dimensional chains ⋮ Topology and bifurcations in Hamiltonian coupled cell systems ⋮ Exact discrete resonances in the Fermi-Pasta-Ulam-Tsingou system ⋮ Time-scales to equipartition in the Fermi-Pasta-Ulam problem: finite-size effects and thermodynamic limit ⋮ Memory effects in the Fermi-Pasta-Ulam model ⋮ Results on normal forms for FPU chains ⋮ On the Korteweg-de Vries limit for the Fermi-Pasta-Ulam system ⋮ On the convergence of the normal form transformation in discrete Rossby and drift wave turbulence ⋮ Tail resonances of Fermi-Pasta-Ulam q-breathers and their impact on the pathway to equipartition ⋮ Coupled oscillator models with no scale separation ⋮ Universal route to thermalization in weakly-nonlinear one-dimensional chains ⋮ Near-integrability of periodic Klein-Gordon lattices ⋮ Korteweg–de Vries and Fermi–Pasta–Ulam–Tsingou: asymptotic integrability of quasi unidirectional waves ⋮ Symmetries of the periodic Toda lattice, with an application to normal forms and perturbations of the lattice with Dirichlet boundary conditions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Exact solutions in the FPU oscillator chain
• On averaging, reduction, and symmetry in Hamiltonian systems
• Near-integrability of periodic FPU-chains
• Poincaré normal and renormalized forms
• Symmetric invariant manifolds in the Fermi-Pasta-Ulam lattice
• Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States
• On the Passage through Resonance
• The symmetries of solitons
• Method for Solving the Korteweg-deVries Equation
• The Toda lattice. II. Existence of integrals
• Symmetry and resonance in periodic FPU chains