Introduction to Classical Integrable Systems

ISBN-13: 9780521822671 / Angielski / Twarda / 2003 / 616 str.

O. Babelon; D. Bernard; M. Talon

Opis

Introducing the reader to classical integrable systems and their applications, this book synthesizes the different approaches to the subject, providing a set of interconnected methods for solving problems in mathematical physics. The authors introduce and explain each method, and demonstrate how it can be applied to particular examples. Rather than presenting an exhaustive list of the various integrable systems, they focus on classical objects which have well-known quantum counterparts, or are the semi-classical limits of quantum objects. They thus enable readers to understand the literature on quantum integrable systems.

Recenzje

'This monograph provides a thorough introduction to the theory of classical integrable systems … The book contains many worked examples and is suitable for use as a textbook on graduate courses. For researchers already working in this field this book is a valuable source of information which provides an excellent overview of the established results and the present developments.' Zentralblatt MATH

Spis treści

1. Introduction; 2. Integrable dynamical systems; 3. Synopsis of integrable systems; 4. Algebraic methods; 5. Analytical methods; 6. The closed Toda chain; 7. The Calogero-Moser model; 8. Isomonodromic deformations; 9. Grassmannian and integrable hierarchies; 10. The KP hierarchy; 11. The KdV hierarchy; 12. The Toda field theories; 13. Classical inverse scattering method; 14. Symplectic geometry; 15. Riemann surfaces; 16. Lie algebras; Index.