**Geometric and Algebraic Structures
in Differential Equations **

edited by

I. S. Krasil'shchik and
Paul Kersten

Reprinted from Acta Applicandae Mathematicae 41:1-3,

Kluwer Academic Publishers, Dordrecht

- Hardbound, ISBN 0-7923-3871-5

November 1995, 356 pp.

NLG 319.00 / USD 191.50 / GBP 124.50

The geometrical theory of nonlinear differential equations
originates from classical works by S. Lie and A. Bäcklund. 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.

- 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 -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, You-Jin Zhang, Walter Strampp.*