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Geometric and Algebraic Structures in Differential Equations
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.
Symmetries and Recursion Operators for Classical and Supersymmetric Differential Equations
To our wives, Masha and Marian Interest in the so-called completely integrable systems with infinite num ber of degrees of freedom was aroused immediately after publication of the famous series of papers by Gardner, Greene, Kruskal, Miura, and Zabusky [75, 77, 96, 18, 66, 19J (see also [76]) on striking properties of the Korteweg-de Vries (KdV) equation. It soon became clear that systems of such a kind possess a number of characteristic properties, such as infinite series of symmetries and/or conservation laws, inverse scattering problem formulation, L - A pair representation, existence of prolongation structures, etc. And though no satisfactory definition of complete integrability was yet i...
Symmetries of Partial Differential Equations
2 The authors of these issues involve not only mathematicians, but also speci alists in (mathematical) physics and computer sciences. So here the reader will find different points of view and approaches to the considered field. A. M. VINOGRADOV 3 Acta Applicandae Mathematicae 15: 3-21, 1989. © 1989 Kluwer Academic Publishers. Symmetries and Conservation Laws of Partial Differential Equations: Basic Notions and Results A. M. VINOORADOV Department of Mathematics, Moscow State University, 117234, Moscow, U. S. S. R. (Received: 22 August 1988) Abstract. The main notions and results which are necessary for finding higher symmetries and conservation laws for general systems of partial differentia...
Expedition Agroparks
This book is the result of several years of expedition into the development of metropolitan FoodClusters. The author's fascination for the agricultural landscapes in and around metropolises led him to the conclusion that improving the efficiency of agriculture is the most effective way to safeguard the quality of such landscapes. The wasteful modes of production developed in the past 150 years have led to a serious decline in both the surface area and the quality of the highly valued landscapes. Closing the loops within the agricultural production system and increasing their productivity is therefore the best remedy to arrest this decline. After analysing the development of agriculture again...
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PASCOS 2004
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SEESAW 25
This volume presents the progress made in the study of the Seesaw mechanism and of its implications over the past 25 years, as well as the recent theoretical developments in the understanding of the measured pattern of neutrino masses and mixings. Observable implications of the Seesaw mechanism like leptogenesis or lepton flavour violation in supersymmetric theories are discussed, and the key aspects of the vast experimental program aimed at determining the neutrino parameters and properties are reviewed. The book provides an up-to-date and in-depth perspective on neutrino masses and on the associated physics in the Seesaw scenario. Contents: Seesaw and the Riddle of Mass (P Ramond)Leptogene...
