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The symbolic computation of integrability structures for partial differential equations

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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  Read more...

Abstract:
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  Read more...

Author(s): VITOLO, RAFFAELE. KRASIL'SHCHIK JOSEPH. VERBOVETSKY ALEXANDER
Publisher: SPRINGER INTERNATIONAL PU
Year: 2017

Language: English
Pages: 272
Tags: Differential equations, Partial.;Logic, Symbolic and mathematical.;Geometry, Differential.;Mathematics.;Difference and Functional Equations.;Math Applications in Computer Science.;Symbolic and Algebraic Manipulation.

Content: 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.