Proof of Nishida's conjecture on anharmonic lattices

Abstract

We prove Nishida's 1971 conjecture stating that almost all low-energetic motions of the anharmonic Fermi-Pasta-Ulam lattice with fixed endpoints are quasi-periodic. The proof is based on the formal computations of Nishida, the KAM theorem, discrete symmetry considerations and an algebraic trick that considerably simplifies earlier results.

arXiv comment16 pages, 1 figure; accepted for publication in Comm. Math. Phys

References in corpus (2)

• Symmetry and resonance in periodic FPU chains
• Symmetric invariant manifolds in the Fermi-Pasta-Ulam lattice

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• Tail resonances of FPU q-breathers and their impact on the pathway to equipartition
• Wave Turbulence and thermalization in one-dimensional chains
• Exact discrete resonances in the Fermi-Pasta-Ulam-Tsingou system
• Memory effects in the Fermi-Pasta-Ulam Model
• Korteweg-de Vries and Fermi-Pasta-Ulam-Tsingou: asymptotic integrability of quasi unidirectional waves
• On the convergence of the normal form transformation in discrete Rossby and drift wave turbulence
• Universal route to thermalization in weakly-nonlinear one-dimensional chains
• Korteweg--de Vries limit for the Fermi--Pasta--Ulam system
• Near-integrability of periodic Klein-Gordon lattices