Invariant Manifolds for a Class of Dispersive, Hamiltonian, Partial Differential Equations

Claude-Alain Pillet (1, 2) , C. Eugene Wayne (3)

1 CPT - Centre de Physique Théorique - UMR 6207
2 CPT - Centre de Physique Théorique - UMR 7332
3 Department of Mathematics

We construct an invariant manifold of periodic orbits for a class of non-linear Schrödinger equations. Using standard ideas of the theory of center manifolds, we rederive the results of Soffer and Weinstein (Comm. Math. Phys.133, 119–146 (1997);J. Differential Equations98, 376–390 (1992)) on the large time asymptotics of small solutions (scattering theory).

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]; Equations aux dérivées partielles [math.AP]; Systèmes dynamiques [math.DS]

Claude-Alain Pillet, C. Eugene Wayne. Invariant Manifolds for a Class of Dispersive, Hamiltonian, Partial Differential Equations. Journal of Differential Equations, 1997, 141, pp.310-326. ⟨10.1006/jdeq.1997.3345⟩. ⟨hal-00129125⟩