Lie algebras, geometry and Toda-type systems
著者
書誌事項
Lie algebras, geometry and Toda-type systems
（Cambridge lecture notes in physics, 8）
Cambridge University Press, 1997
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
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.
目次
- 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.
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