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Introduction to Classical Integrable Systems (Cambridge Monographs on Mathematical Physics) - Hardcover
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.
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Review:
'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
Book Description:
A clear and pedagogical introduction to classical integrable systems and their applications. It synthesizes the different approaches to the subject, providing a set of interconnected methods for solving problems in mathematical physics. Each method is introduced and explained, before being applied to particular examples.
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- PublisherCambridge University Press
- Publication date2003
- ISBN 10 052182267X
- ISBN 13 9780521822671
- BindingHardcover
- Number of pages616
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