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

Abstract : 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.
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Contributor : Simona Rota Nodari <>
Submitted on : Wednesday, July 11, 2018 - 7:36:49 PM
Last modification on : Wednesday, February 27, 2019 - 1:06:49 PM
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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, Springer Verlag, 2019, 231 (1), pp.233-284. ⟨10.1007/s00205-018-1278-5⟩. ⟨hal-01312534v3⟩

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