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The Defocusing NLS Equation and Its Normal Form
Benoît Grébert, University of Nantes, France, and Thomas Kappeler, University of Zurich, Switzerland
A publication of the European Mathematical Society.
cover
EMS Series of Lectures in Mathematics
2014; 176 pp; softcover
Volume: 18
ISBN-10: 3-03719-131-7
ISBN-13: 978-3-03719-131-6
List Price: US$38
Member Price: US$30.40
Order Code: EMSSERLEC/18
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The theme of this monograph is the nonlinear Schrödinger equation. This equation models slowly varying wave envelopes in dispersive media and arises in various physical systems such as water waves, plasma physics, solid state physics and nonlinear optics. More specifically, this book treats the defocusing nonlinear Schrödinger (dNLS) equation on the circle with a dynamical systems viewpoint. By developing the normal form theory, it is shown that this equation is an integrable partial differential equation in the strongest possible sense. In particular, all solutions of the dNLS equation on the circle are periodic, quasi-periodic or almost-periodic in time and Hamiltonian perturbations of this equation can be studied near solutions far away from the equilibrium.

The book is intended not only for specialists working at the intersection of integrable PDEs and dynamical systems but also for researchers farther away from these fields as well as for graduate students. It is written in a modular fashion; each of its chapters and appendices can be read independently of each other.

A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.

Readership

Graduate students and research mathematicians interested in integrable PDEs and dynamical systems.

Table of Contents

  • Zakharov-Shabat operators
  • Spectra
  • Liouville coordinates
  • Birkhoff coordinates
  • Appendices
  • References
  • Index
  • Notations
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