Orbital stability via the energy-momentum method: the case of higher dimensional symmetry groupsReport as inadecuate




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1 LPP - Laboratoire Paul Painlevé 2 MEPHYSTO - Quantitative methods for stochastic models in physics LPP - Laboratoire Paul Painlevé, ULB - Université Libre de Bruxelles Bruxelles, Inria Lille - Nord Europe 3 IMB - Institut de Mathématiques de Bourgogne Dijon

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.





Author: Stephan De Bievre - Simona Rota Nodari -

Source: https://hal.archives-ouvertes.fr/



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