03639nam 22005655 450 991028095060332120200704214452.03-319-71655-710.1007/978-3-319-71655-8(CKB)4530000000000072(MiAaPQ)EBC5341319(DE-He213)978-3-319-71655-8(PPN)226697150(EXLCZ)99453000000000007220180403d2017 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierThe Symbolic Computation of Integrability Structures for Partial Differential Equations /by Joseph Krasil'shchik, Alexander Verbovetsky, Raffaele Vitolo1st ed. 2017.Cham :Springer International Publishing :Imprint: Springer,2017.1 online resource (272 pages)Texts & Monographs in Symbolic Computation, A Series of the Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria,0943-853X3-319-71654-9 Includes bibliographical references and index.Introduction -- Computational problems in the geometry of PDEs -- Old and new Reduce software for integrability of PDEs -- Internal coordinates and total derivatives -- Conservation laws and nonlocal variables -- Cosymmetries -- Symmetries -- The tangent covering -- Recursion operators for symmetries -- Variational symplectic structures -- Cotangent covering -- Variational Poisson structures -- Recursion operators for cosymmetries -- The Plebanski equation -- Discussion.This is the first book devoted to the task of computing integrability structures by computer. The symbolic computation of integrability operator is a computationally hard problem and the book covers a huge number of situations through tutorials. The mathematical part of the book is a new approach to integrability structures that allows to treat all of them in a unified way. The software is an official package of Reduce. Reduce is free software, so everybody can download it and make experiments using the programs available at our website.Texts & Monographs in Symbolic Computation, A Series of the Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria,0943-853XDifference equationsFunctional equationsComputer science—MathematicsDifference and Functional Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12031Math Applications in Computer Sciencehttps://scigraph.springernature.com/ontologies/product-market-codes/I17044Symbolic and Algebraic Manipulationhttps://scigraph.springernature.com/ontologies/product-market-codes/I17052Difference equations.Functional equations.Computer science—Mathematics.Difference and Functional Equations.Math Applications in Computer Science.Symbolic and Algebraic Manipulation.515.353Krasil'shchik Josephauthttp://id.loc.gov/vocabulary/relators/aut1062597Verbovetsky Alexanderauthttp://id.loc.gov/vocabulary/relators/autVitolo Raffaeleauthttp://id.loc.gov/vocabulary/relators/autBOOK9910280950603321The Symbolic Computation of Integrability Structures for Partial Differential Equations2526856UNINA