**CBMS Regional Conference Series in Mathematics**

Volume: 96;
2002;
115 pp;
Softcover

MSC: Primary 58; 35;

Print ISBN: 978-0-8218-2639-3

Product Code: CBMS/96

List Price: $30.00

Individual Price: $24.00

**Electronic ISBN: 978-1-4704-2456-5
Product Code: CBMS/96.E**

List Price: $30.00

Individual Price: $24.00

# Selected Topics in the Geometrical Study of Differential Equations

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*Niky Kamran*

A co-publication of the AMS and CBMS

The geometrical study of differential equations has a long and distinguished
history, dating back to the classical investigations of Sophus Lie, Gaston
Darboux, and Elie Cartan. Currently, these ideas occupy a central position in
several areas of pure and applied mathematics, including the theory of
completely integrable evolution equations, the calculus of variations, and the
study of conservation laws. In this book, the author gives an overview of a
number of significant ideas and results developed over the past decade in the
geometrical study of differential equations.

Topics covered in the book include symmetries of differential equations and
variational problems, the variational bi-complex and conservation laws,
geometric integrability for hyperbolic equations, transformations of
submanifolds and systems of conservation laws, and an introduction to the
characteristic cohomology of differential systems.

The exposition is sufficiently elementary so that non-experts can understand
the main ideas and results by working independently. The book is also suitable
for graduate students and researchers interested in the study of differential
equations from a geometric perspective. It can serve nicely as a companion
volume to The Geometrical Study of Differential Equations, Volume 285 in the AMS series, Contemporary Mathematics.

#### Table of Contents

# Table of Contents

## Selected Topics in the Geometrical Study of Differential Equations

- Cover Cover11 free
- Title iii4 free
- Copyright iv5 free
- Contents vii8 free
- Preface ix10 free
- Acknowledgments xiii14 free
- Chapter 1. Differential equations and their geometry 116 free
- 1. The Cauchy problem for first-order partial differential equations 116
- 2. Hyperbolic equations integrable by the method of Darboux 318
- 3. External, internal and generalized symmetries 520
- 4. The inverse problem of the calculus of variations 621
- 5. Some important topics not covered in these lectures 722

- Chapter 2. External and generalized symmetries 924
- Chapter 3. Internal, external and generalized symmetries 2742
- Chapter 4. Transformations of surfaces 3954
- Chapter 5. Transformations of submanifolds 4762
- Chapter 6. Hamiltonian systems of conservation laws 5772
- Chapter 7. The variational bi-complex 6782
- Chapter 8. The inverse problem of the calculus of variations 7590
- Chapter 9. Conservation laws and Darboux integrability 8398
- Chapter 10. Characteristic cohomology of differential systems 99114
- Bibliography 111126
- Back Cover Back Cover1135

#### Readership

Graduate students and research mathematicians interested in the study of differential equations from a geometric perspective.

#### Reviews

The author performs an outstanding feat of concise exposition … exposition is concise yet informative … the author does a wonderful job in conveying, in a little over 100 pages, some sense of the subject's diversity of ideas and results … written in a clear and lucid style and is recommended as a fine introduction to the geometry of differential equations.

-- Mathematical Reviews