Proof of Nishida's conjecture on anharmonic lattices

Details Proof of Nishida's conjecture on anharmonic lattices Proof of Nishida's conjecture on anharmonic lattices

2005-06-09

arxiv.org/abs/nlin/0506024v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

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

Scientific paper

10.1007/s00220-005-1451-1

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.

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