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

Stephan De Bievre 1, 2 Simona Rota Nodari 3
2 MEPHYSTO - Quantitative methods for stochastic models in physics
LPP - Laboratoire Paul Painlevé - UMR 8524, ULB - Université Libre de Bruxelles [Bruxelles], Inria Lille - Nord Europe
Abstract : We consider the orbital stability of the relative equilibria of Hamiltonian dynamical systems on Banach spaces, in the presence of a multi-dimensional invariance group for the dynamics. We 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 the plane waves of a system of two coupled nonlinear Schrödinger equations. We provide a comparison of our approach to the one by Grillakis-Shatah-Strauss.
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https://hal.archives-ouvertes.fr/hal-01312534
Contributeur : Simona Rota Nodari <>
Soumis le : vendredi 6 mai 2016 - 21:49:42
Dernière modification le : mardi 10 mai 2016 - 10:45:41
Document(s) archivé(s) le : mercredi 25 mai 2016 - 05:50:38

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  • HAL Id : hal-01312534, version 1
  • ARXIV : 1605.02523

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Stephan De Bievre, Simona Rota Nodari. Orbital stability via the energy-momentum method: the case of higher dimensional symmetry groups. 2016. 〈hal-01312534〉

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