Algebraic theory of differential equations /
MacCallum, M. A. H.
Mikhailov, Alexander V.,1953-
London Mathematical Society
application/pdf
"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." "These selected contributions reflect different approaches to the integration of differential equations, originating from Differential Galois Theory, Symmetry, Integrability and Soliton Theory. The ideas of several mathematical communities are here brought together and connections between them sought."--BOOK JACKET.
"This book presents lectures given during a school and workshop organized at Heriot-Watt University in July and August 2006"--Preface.
Includes bibliographical references.
Galois theory of linear differential equations / Michael F. Singer -- Solving in closed form / Felix Ulmer and Jacques-Arthur Weil -- Factorization of linear systems / Sergey P. Tsarev -- Introduction to D-modules / Anton Leykin -- Symbolic representation and classification of integrable systems / A.V. Mikhailov, V.S. Novikov and Jing Ping Wang -- Searching for integrable (P)DEs / Jarmo Hietarinta -- Around differential Galois theory / Anand Pillay.
"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." "These selected contributions reflect different approaches to the integration of differential equations, originating from Differential Galois Theory, Symmetry, Integrability and Soliton Theory. The ideas of several mathematical communities are here brought together and connections between them sought."--BOOK JACKET.
Differential equations
Algebraic number theory
Differential calculus
Differential algebra
Algebraic number theory
Differential algebra
Differential calculus
Differential equations
Algebraic theory