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Lie Algebras, Geometry, and Toda-Type Systems

Lie Algebras, Geometry, and Toda-Type Systems

Part of Cambridge Lecture Notes in Physics

  • Date Published: May 1997
  • availability: Available
  • format: Paperback
  • isbn: 9780521479233

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About the Authors
  • Devoted to an important and popular branch of modern theoretical and mathematical physics, this book introduces the use of Lie algebra and differential geometry methods to study nonlinear integrable systems of Toda type. Many challenging problems in theoretical physics are related to the solution of nonlinear systems of partial differential equations. One of the most fruitful approaches in recent years has resulted from a merging of group algebraic and geometric techniques. The book gives a comprehensive introduction to this exciting branch of science. Chapters 1 and 2 review basic notions of Lie algebras and differential geometry with an emphasis on further applications to integrable nonlinear systems. Chapter 3 contains a derivation of Toda type systems and their general solutions based on Lie algebra and differential geometry methods. The last chapter examines explicit solutions of the corresponding equations. The book is written in an accessible "lecture note" style with many examples and exercises to illustrate key points and to reinforce understanding.

    • First graduate textbook in this fast growing area
    • Author are leading researchers on topics covered in book
    • Text contains much original material as well as many exercises and examples
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    Reviews & endorsements

    "The style is clear and designed for graduate students with basic knowledge of algebra and geometry but it is also of great interest to any physicist or mathematicians working on the interface of mathmatics and physics. The book is of interest for serious practitioners as well as beginners in the field. It should serve as a classical and handy reference for this rapidly developing area of research for some time to come." Henrik Aratyn, Mathematical Reviews

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    Product details

    • Date Published: May 1997
    • format: Paperback
    • isbn: 9780521479233
    • length: 268 pages
    • dimensions: 229 x 152 x 15 mm
    • weight: 0.4kg
    • contains: 1 b/w illus. 4 tables
    • availability: Available
  • Table of Contents

    Preface
    1. Introductory data on Lie algebras
    2. Basic notions of differential geometry
    3. Differential geometry of Toda type systems
    4. Toda type systems and their explicit solutions
    References
    Subject index.

  • Authors

    Alexander V. Razumov, Institute of High-Energy Physics, Protvino, Russia

    Mikhail V. Saveliev, Institute of High-Energy Physics, Protvino, Russia

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