Travelling Waves in a Chain of Coupled Nonlinear Oscillators

Abstract : In a chain of nonlinear oscillators, linearly coupled to their nearest neighbors, all travelling waves of small amplitude are found as solutions of finite dimensional reversible dynamical systems. The coupling constant and the inverse wave speed form the parameter space. The groundstate consists of a one-parameter family of periodic waves. It is realized in a certain parameter region containing all cases of light coupling. Beyond the border of this region the complexity of wave-forms increases via a succession of bifurcations. In this paper we give an appropriate formulation of this problem, prove the basic facts about the reduction to finite dimensions, show the existence of the ground states and discuss the first bifurcation by determining a normal form for the reduced system. Finally we show the existence of nanopterons, which are localized waves with a noncancelling periodic tail at infinity whose amplitude is exponentially small in the bifurcation parameter.
Liste complète des métadonnées

Littérature citée [20 références]  Voir  Masquer  Télécharger

https://hal.univ-cotedazur.fr/hal-01271086
Contributeur : Gerard Iooss <>
Soumis le : mardi 9 février 2016 - 08:34:12
Dernière modification le : jeudi 3 mai 2018 - 13:32:58
Document(s) archivé(s) le : samedi 12 novembre 2016 - 14:26:25

Fichier

Ioki07011.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Citation

Gérard Iooss, Klaus Kirchgässner. Travelling Waves in a Chain of Coupled Nonlinear Oscillators. Communications in Mathematical Physics, Springer Verlag, 2000, 211 (2), pp.26. 〈10.1007/s002200050821〉. 〈hal-01271086〉

Partager

Métriques

Consultations de la notice

422

Téléchargements de fichiers

93