Krasil'shchik, Joseph. The Symbolic Computation of Integrability Structures for Partial Differential Equations [electronic resource] / / by Joseph Krasil'shchik, Alexander Verbovetsky, Raffaele Vitolo.. — 1st ed. 2017.. — XV, 263 p. 28 illus. : online resource. — (Texts & Monographs in Symbolic Computation, A Series of the Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria,) 0943-853X. - Texts & Monographs in Symbolic Computation, A Series of the Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria, .
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.
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Анотація: 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.
9783319716558
10.1007/978-3-319-71655-8 doi
Difference equations. Functional equations. Computer science—Mathematics. Difference and Functional Equations. Math Applications in Computer Science. Symbolic and Algebraic Manipulation.