Introduction to classical integrable systems
US$5.00 US$19.00Title (user) : Introduction to classical integrable systemsISBN : 9780521822671,052182267XGoogleBook ID : Hboa9NvpvdACOpenLibrary ID : OL22527402MEdition : web draftSeries : Cambridge Monographs on Mathematical PhysicsAuthors (user) : Olivier Babelon, Denis Bernard, Michel...
Title (user) : Introduction to classical integrable systems
ISBN : 9780521822671,052182267X
GoogleBook ID : Hboa9NvpvdAC
OpenLibrary ID : OL22527402M
Edition : web draft
Series : Cambridge Monographs on Mathematical Physics
Authors (user) : Olivier Babelon, Denis Bernard, Michel Talon
Authors (google) : Olivier Babelon,Denis Bernard,Michel Talon
Publisher : Cambridge University Press
Language : English
Publication Date : 2003
File Format : gz
Categories : Mathematics
Description (user) :
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.
Description (google) :
This book provides a thorough introduction to the theory of classical integrable systems, discussing the various approaches to the subject and explaining their interrelations. The book begins by introducing the central ideas of the theory of integrable systems, based on Lax representations, loop groups and Riemann surfaces. These ideas are then illustrated with detailed studies of model systems. The connection between isomonodromic deformation and integrability is discussed, and integrable field theories are covered in detail. The KP, KdV and Toda hierarchies are explained using the notion of Grassmannian, vertex operators and pseudo-differential operators. A chapter is devoted to the inverse scattering method and three complementary chapters cover the necessary mathematical tools from symplectic geometry, Riemann surfaces and Lie algebras. The book contains many worked examples and is suitable for use as a textbook on graduate courses. It also provides a comprehensive reference for researchers already working in the field.