Orbital stability via the energy-momentum ...
Document type :
Compte-rendu et recension critique d'ouvrage
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]
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
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]
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 >
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
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