Algebraic Theory of Differential Equations

by Edited by Malcolm A. H. MacCallum , Alexander V. Mikhailov

• ISBN13: 9780521720083
• ISBN10: 0521720087
• Edition: 1st
• Format: Paperback
• Copyright: 2009-01-05
• Publisher: Cambridge University Press

Summary

Integration of differential equations is a central problem in mathematics and several approaches have been developed by studying analytic, algebraic, and algorithmic aspects of the subject. One of these is Differential Galois Theory, developed by Kolchin and his school, and another originates from the Soliton Theory and Inverse Spectral Transform method, which was born in the works of Kruskal, Zabusky, Gardner, Green and Miura. Many other approaches have also been developed, but there has so far been no intersection between them. This unique introduction to the subject finally brings them together, with the aim of initiating interaction and collaboration between these various mathematical communities. The collection includes a LMS Invited Lecture Course by Michael F. Singer, together with some shorter lecture courses and review articles, all based upon a mini-program held at the International Centre for Mathematical Sciences (ICMS) in Edinburgh.

Table of Contents

Preface	p. vi
Galois Theory of Linear Differential Equations	p. 1
Solving in closed form	p. 83
Factorization of Linear Systems	p. 111
Introduction to D-modules	p. 132
Symbolic representation and classification of integrable systems	p. 156
Searching for integrable (P)DEs	p. 217
Around Differential Galois Theory	p. 232
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