Title :

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

Author(s) :

De Bievre, Stephan [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Méthodes quantitatives pour les modèles aléatoires de la physique [MEPHYSTO-POST]
Rota Nodari, Simona [Auteur]
Institut de Mathématiques de Bourgogne [Dijon] [IMB]

Journal title :

Archive for Rational Mechanics and Analysis

Pages :

233-284

Publisher :

Springer Verlag

Publication date :

2019-01-22

ISSN :

0003-9527

English keyword(s) :

hamiltonian relative equilibria
standing waves
solitary waves
instabilities
systems
persistence
states

HAL domain(s) :

Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Mathématiques [math]/Systèmes dynamiques [math.DS]
Mathématiques [math]/Géométrie symplectique [math.SG]

English abstract : [en]

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 ...
Show more >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.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL