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Applied Mathematical Sciences

Invariant Manifolds and Fibrations for Perturbed Nonlinear Schrödinger Equations

Authors: Li, Charles, Wiggins, Stephen

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About this book

This book presents a development of invariant manifold theory for a spe­ cific canonical nonlinear wave system -the perturbed nonlinear Schrooinger equation. The main results fall into two parts. The first part is concerned with the persistence and smoothness of locally invariant manifolds. The sec­ ond part is concerned with fibrations of the stable and unstable manifolds of inflowing and overflowing invariant manifolds. The central technique for proving these results is Hadamard's graph transform method generalized to an infinite-dimensional setting. However, our setting is somewhat different than other approaches to infinite dimensional invariant manifolds since for conservative wave equations many of the interesting invariant manifolds are infinite dimensional and noncom pact. The style of the book is that of providing very detailed proofs of theorems for a specific infinite dimensional dynamical system-the perturbed nonlinear Schrodinger equation. The book is organized as follows. Chapter one gives an introduction which surveys the state of the art of invariant manifold theory for infinite dimensional dynamical systems. Chapter two develops the general setup for the perturbed nonlinear Schrodinger equation. Chapter three gives the proofs of the main results on persistence and smoothness of invariant man­ ifolds. Chapter four gives the proofs of the main results on persistence and smoothness of fibrations of invariant manifolds. This book is an outgrowth of our work over the past nine years concerning homoclinic chaos in the perturbed nonlinear Schrodinger equation. The theorems in this book provide key building blocks for much of that work.

Table of contents (4 chapters)

  • Introduction

    Li, Charles (et al.)

    Pages 1-11

  • The Perturbed Nonlinear Schrödinger Equation

    Li, Charles (et al.)

    Pages 13-33

  • Persistent Invariant Manifolds

    Li, Charles (et al.)

    Pages 35-62

  • Fibrations of the Persistent Invariant Manifolds

    Li, Charles (et al.)

    Pages 63-159

Buy this book

eBook $79.99
price for USA in USD (gross)
  • ISBN 978-1-4612-1838-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $119.99
price for USA in USD
  • ISBN 978-0-387-94925-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $99.99
price for USA in USD
  • ISBN 978-1-4612-7307-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Invariant Manifolds and Fibrations for Perturbed Nonlinear Schrödinger Equations
Authors
Series Title
Applied Mathematical Sciences
Series Volume
128
Copyright
1997
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4612-1838-8
DOI
10.1007/978-1-4612-1838-8
Hardcover ISBN
978-0-387-94925-3
Softcover ISBN
978-1-4612-7307-3
Series ISSN
0066-5452
Edition Number
1
Number of Pages
VIII, 172
Topics