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

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).