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Selected Topics in the Geometrical Study of Differential Equations
Niky Kamran, McGill University, Montreal, QC, Canada
A co-publication of the AMS and CBMS.
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CBMS Regional Conference Series in Mathematics
2002; 115 pp; softcover
Number: 96
ISBN-10: 0-8218-2639-5
ISBN-13: 978-0-8218-2639-3
List Price: US$28
Member Price: US$22.40
All Individuals: US$22.40
Order Code: CBMS/96
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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.

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

Table of Contents

  • Differential equations and their geometry
  • External and generalized symmetries
  • Internal, external and generalized symmetries
  • Transformations of surfaces
  • Tranformations of submanifolds
  • Hamiltonian systems of conservation laws
  • The variational bi-complex
  • The inverse problem of the calculus of variations
  • Conservation laws and Darboux integrability
  • Characteristic cohomology of differential systems
  • Bibliography
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