Geometry and Integrability

Erscheinungsjahr 2003
ISBN: 978-0-521-52999-0
Verlag: Cambridge University Press

Buch, Englisch, Band 295, 166 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 251 g

Reihe: London Mathematical Society Lecture Note Series

Most integrable systems owe their origin to problems in geometry and they are best understood in a geometrical context. This is especially true today when the heroic days of KdV-type integrability are over. Problems that can be solved using the inverse scattering transformation have reached the point of diminishing returns. Two major techniques have emerged for dealing with multi-dimensional integrable systems: twistor theory and the d-bar method, both of which form the subject of this book. It is intended to be an introduction, though by no means an elementary one, to current research on integrable systems in the framework of differential geometry and algebraic geometry. This book arose from a seminar, held at the Feza Gursey Institute, to introduce advanced graduate students to this area of research. The articles are all written by leading researchers and are designed to introduce the reader to contemporary research topics.

Autoren/Hrsg.

Mason, Lionel

Nutku, Yavuz

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik EDV | Informatik Professionelle Anwendung Computer-Aided Design (CAD)
• Mathematik | Informatik EDV | Informatik Angewandte Informatik Computeranwendungen in Wissenschaft & Technologie
• Mathematik | Informatik Mathematik Geometrie Elementare Geometrie: Allgemeines
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
• Mathematik | Informatik Mathematik Topologie Mengentheoretische Topologie
• Technische Wissenschaften Technik Allgemein Computeranwendungen in der Technik

Inhaltsverzeichnis

1. Introduction Lionel Mason; 2. Differential equations featuring many periodic solutions F. Calogero; 3. Geometry and integrability R. Y. Donagi; 4. The anti self-dual Yang-Mills equations and their reductions Lionel Mason; 5. Curvature and integrability for Bianchi-type IX metrics K. P. Tod; 6. Twistor theory for integrable equations N. M. J. Woodhouse; 7. Nonlinear equations and the d-bar problem P. Santini.