The Symbolic Computation of Integrability Structures for Partial Differential Equations

• Main Authors: Krasil'shchik, Joseph (Author, http://id.loc.gov/vocabulary/relators/aut), Verbovetsky, Alexander (http://id.loc.gov/vocabulary/relators/aut), Vitolo, Raffaele (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2017.
• Edition: 1st ed. 2017.
• Series: Texts & Monographs in Symbolic Computation, A Series of the Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria,
• Subjects: Difference equations.; Functional equations.; Computer science-Mathematics.; Difference and Functional Equations.; Math Applications in Computer Science.; Symbolic and Algebraic Manipulation.

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...

Table of Contents:

• 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.