Geometric Approaches to Differential Equations

ISBN-13: 9780521775984 / Angielski / Miękka / 2000 / 238 str.

Peter J. Vassiliou; Ian G. Lisle; Peter J. Vassiliou

Opis

Here is a concise and accessible exposition of a wide range of topics in geometric approaches to differential equations. The authors present an overview of this developing subject and introduce a number of related topics, including twistor theory, vortex filament dynamics, calculus of variations, exterior differential systems and Backlund transformations. The book is an ideal starting point for graduate students embarking on research.

Recenzje

'It is a pleasure to report on this outstanding collection of articles … a coherent set of expository lecture notes prepared by leading experts in the geometric aspects of differential equations.' Australian Mathematical Society Gazette

Spis treści

Preface; 1. Geometric approaches to differential equations: an introduction Peter J. Vassiliou; 2. Bäcklund and his works: applications in soliton theory Colin Rogers, Wolfgang K. Schief and Mark E. Johnston; 3. Recent developments in integrable curve dynamics Annalisa Calini; 4. An elementary introduction to exterior differential systems Niky Kamran; 5. Cartan structure of infinite Lie pseudogroups Ian G. Lisle and Gregory J. Reid; 6. Cartan's method of equivalence David Hartley; 7. The inverse problem in the calculus of variations and its ramifications Geoff E. Prince; 8. Twistor theory Michael K. Murray.