The Symbolic Computation of Integrability Structures for Partial Differential Equations

Joseph Krasil'shchik, Alexander Verbovetsky, Raffaele Vitolo (Autoren)

Buch | Softcover

XV, 263 Seiten

2018 | 1. Softcover reprint of the original 1st ed. 2017
Springer International Publishing (Verlag)
978-3-030-10088-9 (ISBN)

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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 Reduce. Reduce is free software, so everybody can download it and make experiments using the programs available at our website.

Joseph Krasil'shchik is a principal researcher at the Institute of Control Sciences of Russian Academy of Sciences and a full professor at the Independent University of Moscow. Alexander Verbovetsky is a lecturer at the Independent University of Moscow. Raffaele Vitolo is an associate professor in mathematical physics at the Department of Mathematics and Physics 'E. De Giorgi' of the Università del Salento.

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.

Erscheint lt. Verlag	9.12.2018
Reihe/Serie	Texts & Monographs in Symbolic Computation
Zusatzinfo	XV, 263 p. 28 illus.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	433 g
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Computerprogramme / Computeralgebra
Schlagworte	geometry of jet spaces • Hamiltonian operators • Integrable Systems • Recursion Operators • Symplectic operators
ISBN-10	3-030-10088-X / 303010088X
ISBN-13	978-3-030-10088-9 / 9783030100889
Zustand	Neuware