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Introduction to Classical Integrable Systems

Introduction to Classical Integrable Systems

£125.00

Part of Cambridge Monographs on Mathematical Physics

  • Date Published: April 2003
  • availability: Available
  • format: Hardback
  • isbn: 9780521822671

£ 125.00
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  • 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.

    • Discusses all approaches to the subject and emphasises their unity
    • Written in a clear and pedagogical style
    • Includes developments of importance for the study of quantum systems
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    Reviews & endorsements

    '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

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    Product details

    • Date Published: April 2003
    • format: Hardback
    • isbn: 9780521822671
    • length: 616 pages
    • dimensions: 254 x 178 x 33 mm
    • weight: 1.28kg
    • contains: 11 b/w illus. 3 tables
    • availability: Available
  • Table of Contents

    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.

  • Authors

    Olivier Babelon, Université de Paris VI (Pierre et Marie Curie) et VII
    Olivier Babelon has been a member of the Centre National de la Recherche Scientifique (CNRS) since 1978. He works at the Laboratoire de Physique Théorique et Hautes Energies (LPTHE) at the University of Paris VI-Paris VII. His main fields of interest are particle physics, gauge theories and integrables systems.

    Denis Bernard, SPHT, CE Saclay
    Denis Bernard has been a member of the CNRS since 1988. He currently works at the Service de Physique Théorique de Saclay. His main fields of interest are conformal field theories and integrable systems, and other aspects of statistical field theories, including statistical turbulence.

    Michel Talon, Université de Paris VI (Pierre et Marie Curie) et VII
    Michel Talon has been a member of the CNRS since 1977. He works at the LPTHE at the University of Paris VI-Paris VII. He is involved in the computation of radiative corrections and anomalies in gauge theories and integrable systems.

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