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Author:   Charles Li ,  Stephen Wiggins
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   1997 ed.
Volume:   128
Dimensions:   Width: 15.50cm , Height: 1.20cm , Length: 23.50cm
Weight:   0.980kg
ISBN:  

9780387949253

ISBN 10:   0387949259
Pages:   172
Publication Date:   23 October 1997
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

1 Introduction.- 1.1 Invariant Manifolds in Infinite Dimensions.- 1.2 Aims and Scope of This Monograph.- 2 The Perturbed Nonlinear Schrödinger Equation.- 2.1 The Setting for the Perturbed Nonlinear Schrödinger Equation.- 2.2 Spatially Independent Solutions: An Invariant Plane.- 2.3 Statement of the Persistence and Fiber Theorems.- 2.4 Explicit Representations for Invariant Manifolds and Fibers.- 2.5 Coordinates Centered on the Resonance Circle.- 2.6 (6 = 0) Invariant Manifolds and the Introduction of a Bump Function.- 3 Persistent Invariant Manifolds.- 3.1 Statement of the Persistence Theorem and the Strategy of Proof.- 3.2 Proof of the Persistence Theorems.- 3.3 The Existence of the Invariant Manifolds.- 3.4 Smoothness of the Invariant Manifolds.- 3.5 Completion of the Proof of the Proposition.- 4 Fibrations of the Persistent Invariant Manifolds.- 4.1 Statement of the Fiber Theorem and the Strategy of Proof.- 4.2 Rate Lemmas.- 4.3 The Existence of an Invariant Subbundle E.- 4.4 Smoothness of the Invariant Subbundle E.- 4.5 Existence of Fibers.- 4.6 Smoothness of the Fiber fE(Q) as a Submanifold.- 4.7 Metric Characterization of the Fibers.- 4.8 Smoothness of Fibers with Respect to the Base Point.- References.

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