Sobolev stability of plane wave solutions to the cubic nonlinear Schrödinger equation on a torus

Erwan Faou 1, 2, * Ludwig Gauckler 3 Christian Lubich 4
* Auteur correspondant
1 IPSO - Invariant Preserving SOlvers
IRMAR - Institut de Recherche Mathématique de Rennes, Inria Rennes – Bretagne Atlantique
Abstract : It is shown that plane wave solutions to the cubic nonlinear Schrödinger equation on a torus behave orbitally stable under generic perturbations of the initial data that are small in a high-order Sobolev norm, over long times that extend to arbitrary negative powers of the smallness parameter. The perturbation stays small in the same Sobolev norm over such long times. The proof uses a Hamiltonian reduction and transformation and, alternatively, Birkhoff normal forms or modulated Fourier expansions in time.
Type de document :
Article dans une revue
Communications in Partial Differential Equations, Taylor & Francis, 2013, 38 (7), pp.1123-1140. <10.1080/03605302.2013.785562>


https://hal.archives-ouvertes.fr/hal-00622240
Contributeur : Marie-Annick Guillemer <>
Soumis le : jeudi 11 octobre 2012 - 14:38:53
Dernière modification le : jeudi 20 octobre 2016 - 11:57:44

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Erwan Faou, Ludwig Gauckler, Christian Lubich. Sobolev stability of plane wave solutions to the cubic nonlinear Schrödinger equation on a torus. Communications in Partial Differential Equations, Taylor & Francis, 2013, 38 (7), pp.1123-1140. <10.1080/03605302.2013.785562>. <hal-00622240v2>

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