Geometry and Integrability
Seiten
2003
Cambridge University Press (Verlag)
978-0-521-52999-0 (ISBN)
Cambridge University Press (Verlag)
978-0-521-52999-0 (ISBN)
Based on a seminar for graduates held at the Feza Gürsey Institute, there are articles by some key researchers. One attractive feature is the inclusion of the algebro-geometric material as well as the twistor space methods, which form a bridge between the pure mathematics and the more physical approaches.
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.
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.
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.
Erscheint lt. Verlag | 20.11.2003 |
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Reihe/Serie | London Mathematical Society Lecture Note Series |
Verlagsort | Cambridge |
Sprache | englisch |
Maße | 154 x 228 mm |
Gewicht | 290 g |
Themenwelt | Mathematik / Informatik ► Mathematik ► Angewandte Mathematik |
Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
ISBN-10 | 0-521-52999-9 / 0521529999 |
ISBN-13 | 978-0-521-52999-0 / 9780521529990 |
Zustand | Neuware |
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