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Titlebook: Geometric and Algebraic Structures in Differential Equations; P. H. M. Kersten,I. S. Krasil’Shchik Book 1995 Kluwer Academic Publishers 19

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书目名称Geometric and Algebraic Structures in Differential Equations
编辑P. H. M. Kersten,I. S. Krasil’Shchik
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图书封面Titlebook: Geometric and Algebraic Structures in Differential Equations;  P. H. M. Kersten,I. S. Krasil’Shchik Book 1995 Kluwer Academic Publishers 19
描述The geometrical theory of nonlinear differential equationsoriginates from classical works by S. Lie and A. Bäcklund. Itobtained a new impulse in the sixties when the complete integrabilityof the Korteweg-de Vries equation was found and it became clearthat some basic and quite general geometrical and algebraic structuresgovern this property of integrability. .Nowadays the geometrical and algebraic approach to partialdifferential equations constitutes a special branch of modernmathematics. .In 1993, a workshop on algebra and geometry of differential equationstook place at the University of Twente (The Netherlands), where thestate-of-the-art of the main problems was fixed. This book contains acollection of invited lectures presented at this workshop. Thematerial presented is of interest to those who work in pure andapplied mathematics and especially in mathematical physics.
出版日期Book 1995
关键词Dimension; Grad; differential equation; hyperbolic equation; partial differential equation; ordinary diff
版次1
doihttps://doi.org/10.1007/978-94-009-0179-7
isbn_softcover978-94-010-6565-8
isbn_ebook978-94-009-0179-7
copyrightKluwer Academic Publishers 1995
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Geometric and Algebraic Structures in Differential Equations978-94-009-0179-7
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Introduction, arose in summer 1992, when one of the editors (P.K.) was visiting the other editor (J.K.) in Moscow. The basic idea was to bring closer and intensify activities of mathematicians and mathematical physicists doing research in this field. The decision was taken that it would be a small workshop for s
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The Cohomology of Invariant Variational Bicomplexes,mology of the Γ invariant variational bicomplex (Ω.(..(.)),d.,d.) and the associated Γ invariant Euler-Lagrange complex. As one application of our general theory, we completely solve the local invariant inverse problem of the calculus of variations for finite-dimensional infinitesimal Lie transforma
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The Use of Factors to Discover Potential Systems or Linearizations,he notion of potential conservation laws, arising from specific types of factors, which lead to useful potential systems. Point symmetries of a potential system could yield nonlocal symmetries of the given system and its linearization by a noninvertible mapping. We also introduce the notion of linea
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A Method for Computing Symmetries and Conservation Laws of Integro-Differential Equations,equation to a system of boundary differential equations and in computing symmetries and conservation laws of this system. A geometry of boundary differential equations is constructed like the differential case. Results of the computation for the Smoluchowski’s coagulation equation are given.
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Graded Differential Equations and Their Deformations: A Computational Theory for Recursion Operatorraded Frölicher-Nijenhuis bracket cohomological invariants ..(.) are related to each object (.,∇) of the theory. Within this framework, ...) generalizes the Lie algebra of symmetries for PDE’s, while ..(.) are identified with equivalence classes of infinitesimal deformations. It is shown that elemen
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