Orbital stability via the energy-momentum method: the case of higher dimensional symmetry groups - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Archive for Rational Mechanics and Analysis Année : 2019

Orbital stability via the energy-momentum method: the case of higher dimensional symmetry groups

Résumé

We consider the orbital stability of relative equilibria of Hamiltonian dynamical systems on Banach spaces, in the presence of a multi-dimensional invariance group for the dynamics. We prove a persistence result for such relative equilibria, present a generalization of the Vakhitov-Kolokolov slope condition to this higher dimensional setting, and show how it allows to prove the local coercivity of the Lyapunov function, which in turn implies orbital stability. The method is applied to study the orbital stability of relative equilibria of nonlinear Schrödinger and Manakov equations. We provide a comparison of our approach to the one by Grillakis-Shatah-Strauss.
Fichier principal
Vignette du fichier
energymomentum_revision_20180625hal.pdf (422.57 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01312534 , version 1 (06-05-2016)
hal-01312534 , version 2 (05-02-2018)
hal-01312534 , version 3 (11-07-2018)

Identifiants

Citer

Stephan de Bièvre, Simona Rota Nodari. Orbital stability via the energy-momentum method: the case of higher dimensional symmetry groups. Archive for Rational Mechanics and Analysis, 2019, 231 (1), pp.233-284. ⟨10.1007/s00205-018-1278-5⟩. ⟨hal-01312534v3⟩
379 Consultations
140 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More