Invariant Manifolds and Fibrations for Perturbed Nonlinear Schrödinger Equations

Hardcover | October 23, 1997

byCharles Li, Stephen Wiggins

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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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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 b...

Format:HardcoverDimensions:180 pages, 9.25 × 6.1 × 0.04 inPublished:October 23, 1997Publisher:Springer New York

The following ISBNs are associated with this title:

ISBN - 10:0387949259

ISBN - 13:9780387949253

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Table of Contents

Introduction.- Invariant Manifolds in Infinite Dimensions. Aims and Scopes of This Monograph.- The Perturbed Nonlinear Schroedinger Equation. The Setting for the Perturbed Nonlinear Schroedinger Equation. Spatially Independent Solutions: An Invariant Plane. Statement of the Persistence and Fiber Theorems. Explicit Representations for Invariant Manifolds and Fibers. Coordinates Centered on the Resonance Circle. Definition of the H Norms. A Neighborhood of the Circle of Fixed Points. An Enlarged Phase Space. Scales through _. The Equations in their Final Setting. (_=0) Invariant Manifolds and the Introduction of a Bump Function. (_=0) Invariant Manifolds.