In this monograph the authors present detailed and pedagogic proofs
of persistence theorems for normally hyperbolic invariant manifolds
and their stable and unstable manifolds for classes of
perturbations of the NLS equation, as well as for the existence and
persistence of fibrations of these invariant manifolds. Their
techniques are based on an infinite dimensional generalisation of
the graph transform and can be viewed as an infinite dimensional
generalisation of Fenichels results. As such, they may be applied
to a broad class of infinite dimensional dynamical systems.
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