Geometric and Algebraic Structures in Differential Equations

ISBN-13: 9789401065658 / Angielski / Miękka / 2011 / 349 str.

P.H.M. Kersten;I.S. Krasil'shchik

Opis

The geometrical theory of nonlinear differential equations originates from classical works by S. Lie and A. Backlund. It obtained a new impulse in the sixties when the complete integrability of the Korteweg-de Vries equation was found and it became clear that some basic and quite general geometrical and algebraic structures govern this property of integrability.
Nowadays the geometrical and algebraic approach to partial differential equations constitutes a special branch of modern mathematics.
In 1993, a workshop on algebra and geometry of differential equations took place at the University of Twente (The Netherlands), where the state-of-the-art of the main problems was fixed. This book contains a collection of invited lectures presented at this workshop. The material presented is of interest to those who work in pure and applied mathematics and especially in mathematical physics."

Spis treści

Introduction; P. Kersten, J. Krasil'shchik. The Cohomology of Invariant Variational Bicomplexes; I.M. Anderson, J. Pohjanpelto. The Use of Factors to Discover Potential Systems of Linearizations; G. Bluman, P. Doran-Wu. A Method for Computing Symmetries and Conservation Laws of Integro-Differential Equations; V.N. Chetverikov, A.G. Kudryavtsev. Multiparameter Quantum Groups and Multiparameter R-Matrices; M. Hazewinkel. Infinite-Dimensional Flag Manifolds in Integrable Systems; G.F. Helminck, A.G. Helminck. Computation by Computer of Lie Superalgebra Homology and Cohomology; N. v.d. Hijligenberg, G.F. Post. Conservation Laws and the Variational Bicomplex for Second-Order Scalar Hyperbolic Equations in the Plane; I.M. Anderson, N. Kamran. On the C-Spectral Sequence for Systems of Evolution Equations; N.G. Khor'kova. Exact Gerstenhaber Algebras and Lie Bialgebroids; Y. Kosmann-Schwarzbach. Graded Differential Equations and their Deformations: A Computational Theory for Recursion Operators; I.S. Krasil'shchik, P.H.M. Kersten. Colour Calculus and Colour Quantizations; V. Lychagin. Spencer Cohomologies and Symmetry Groups; V. Lychagin, L. Zilbergleit. On the Geometry of Soliton Equations; F. Magri. Differential Invariants; P.J. Olver. Spencer Sequence and Variational Sequence; J.F. Pommaret. Super Toda Lattices; E.D. van der Lende, H.G.J. Pijls. Decay of Conservation Laws and their Generating Functions; A.V. Samokhin. Arbitrariness of the General Solution and Symmetries; W.M. Seiler. Deformations of Nonassociative Algebras and Integrable Differential Equations; V.V. Sokolov, S.I. Svinolupov. Constraints of the KP Hierarchy and the Bilinear Method; Yi Cheng, et al.