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The Symbolic Computation of Integrability Structures for Partial Differential Equations de Joseph Krasil'shchik

The Symbolic Computation of Integrability Structures for Partial Differential Equations: Texts & Monographs in Symbolic Computation

Autor Joseph Krasil'shchik, Alexander Verbovetsky, Raffaele Vitolo
en Limba Engleză Paperback – 9 dec 2018
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.
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Specificații

ISBN-13: 9783030100889
ISBN-10: 303010088X
Pagini: 263
Ilustrații: XV, 263 p. 28 illus.
Dimensiuni: 155 x 235 mm
Ediția:Softcover reprint of the original 1st ed. 2017
Editura: Springer International Publishing
Colecția Springer
Seria Texts & Monographs in Symbolic Computation

Locul publicării:Cham, Switzerland

Cuprins

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.

Notă biografică

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.

Textul de pe ultima copertă

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.

Caracteristici

Proposes a new approach and new software for computations Discusses example programs Represents the only book on integrable systems and symbolic computations of integrability operators