Selected Topics in the Geometrical Study of Differential Equations
About this Title
Niky Kamran, McGill University, Montreal, QC, Canada
Publication: CBMS Regional Conference Series in Mathematics
Publication Year 2002: Volume 96
ISBNs: 978-0-8218-2639-3 (print); 978-1-4704-2456-5 (online)
MathSciNet review: MR1908466
MSC: Primary 58J70; Secondary 34A26, 35A22, 35F20, 35L65, 37K25, 58A15
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. 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. The book is also suitable for graduate students and researchers interested in the study of differential equations from a geometric perspective.
Graduate students and research mathematicians interested in the study of differential equations from a geometric perspective.
Table of Contents
- Chapter 1. Differential equations and their geometry
- Chapter 2. External and generalized symmetries
- Chapter 3. Internal, external and generalized symmetries
- Chapter 4. Transformations of surfaces
- Chapter 5. Tranformations of submanifolds
- Chapter 6. Hamiltonian systems of conservation laws
- Chapter 7. The variational bi-complex
- Chapter 8. The inverse problem of the calculus of variations
- Chapter 9. Conservation laws and Darboux integrability
- Chapter 10. Characteristic cohomology of differential systems