Invariant manifolds for a class of dispersive, Hamiltonian, partial differential equations

摘要

We construct an invariant manifold of periodic orbits for a class of non-linear Schrodinger 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 Equations 98, 376-390 (1992)) on the large time asymptotics of small solutions (scattering theory). (C) 1997 Academic Press.