عنوان
پدید آورنده
موضوع
رده
QA377
QA377
کتابخانه
محل استقرار
INTERNATIONAL STANDARD BOOK NUMBER
(Number (ISBN
3319716549
(Number (ISBN
3319716557
(Number (ISBN
9783319716541
(Number (ISBN
9783319716558
Erroneous ISBN
9783319716541
TITLE AND STATEMENT OF RESPONSIBILITY
Title Proper
The symbolic computation of integrability structures for partial differential equations /
General Material Designation
[Book]
First Statement of Responsibility
Joseph Krasil'shchik, Alexander Verbovetsky, Raffaele Vitolo.
.PUBLICATION, DISTRIBUTION, ETC
Place of Publication, Distribution, etc.
Cham :
Name of Publisher, Distributor, etc.
Springer,
Date of Publication, Distribution, etc.
[2017]
PHYSICAL DESCRIPTION
Specific Material Designation and Extent of Item
1 online resource
SERIES
Series Title
Texts and monographs in symbolic computation
CONTENTS NOTE
Text of Note
Intro; Preface; Contents; Introduction; 1 Computational Problems and Dedicated Software; 1.1 Computational Problems in the Geometry of PDEs and Integrability; 1.2 Reduce Software for the Geometry of PDEs and Integrability; 1.3 Other Software for the Geometry of PDEs and Integrability; 2 Internal Coordinates and Total Derivatives; 2.1 General Theory; 2.1.1 C-Differential Operators; 2.1.2 The Linearization Operator and Its Adjoint; 2.2 CDE Implementation; 2.2.1 CDE Jet Space; 2.2.2 CDE and Differential Equations; 2.2.3 CDE and C-Differential Operators; 2.3 Examples
Text of Note
2.3.1 Korteweg-de Vries Equation2.3.2 Dispersionless Boussinesq System; 2.3.3 Camassa-Holm Equation; 2.3.4 Multi-dimensional Examples; 2.3.4.1 Kadomtsev-Petviashvili Equation; 2.3.4.2 Plebanski Equation; 3 Conservation Laws and Nonlocal Variables; 3.1 General Theory; 3.1.1 Conservation Laws; 3.1.2 Nonlocal Variables; 3.2 Examples; 3.2.1 Korteweg-de Vries Equation; 3.2.2 Dispersionless Boussinesq System; 3.2.3 Camassa-Holm Equation; 3.2.4 Gibbons-Tsarev Equation; 3.2.5 Multi-dimensional Examples; 3.2.5.1 Universal Hierarchy Equation; 3.2.5.2 Khokhlov-Zabolotskaya Equation; 4 Cosymmetries
Text of Note
4.1 General Theory; 4.1.1 Generating Functions of Conservation Laws; 4.1.2 Reconstruction of Conservation Laws by Their Generating Functions; 4.2 Examples; 4.2.1 Korteweg-de Vries Equation; 4.2.2 Dispersionless Boussinesq System; 4.2.3 Camassa-Holm Equation; 4.2.4 Gibbons-Tsarev Equation; 4.2.5 Multi-dimensional Examples; 4.2.5.1 Universal hierarchy Equation; 4.2.5.2 Khokhlov-Zabolotskaya Equation; 5 Symmetries; 5.1 General Theory; 5.1.1 Local Symmetries; 5.1.2 Jacobi Bracket; 5.1.3 Reductions and Invariant Solutions; 5.1.4 Nonlocal Symmetries and Shadows; 5.2 Examples
Text of Note
5.2.1 Korteweg-de Vries Equation5.2.2 Burgers Equation; 5.2.3 Dispersionless Boussinesq System; 5.2.4 Camassa-Holm Equation; 5.2.5 Multi-dimensional Examples; 5.2.5.1 Universal Hierarchy Equation; 5.2.5.2 Pavlov Equation; 6 The Tangent Covering; 6.1 General Theory; 6.2 Examples; 6.2.1 Korteweg-de Vries Equation; 6.2.2 Dispersionless Boussinesq System; 6.2.3 Camassa-Holm Equation; 6.2.4 Multi-dimensional Examples; 6.2.4.1 The Kadomtsev-Petviashvili Equation; 6.2.4.2 The Plebanski Equation; 7 Recursion Operators for Symmetries; 7.1 General Theory; 7.1.1 Variational Nijenhuis Bracket
Text of Note
7.1.2 Hereditary Operators7.1.3 Recursion Operators as Bäcklund Transformations; 7.2 Examples; 7.2.1 Korteweg-de Vries Equation; 7.2.2 Dispersionless Boussinesq System; 7.2.3 Camassa-Holm Equation; 7.2.4 Heat Equation; 7.2.5 Multi-dimensional Examples; 7.2.5.1 The Plebanski Equation; 7.2.5.2 The rdDym Equation; 7.2.5.3 The Pavlov Equation; 7.2.5.4 The Universal Hierarchy Equation; 8 Variational Symplectic Structures; 8.1 General Theory; 8.2 Examples; 8.2.1 The Two-Dimensional WDVV Equation; 8.2.2 The Krichever-Novikov Equation; 8.2.3 Korteweg-de Vries Equation
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SUMMARY OR ABSTRACT
Text of Note
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.
ACQUISITION INFORMATION NOTE
Source for Acquisition/Subscription Address
Springer Nature
Stock Number
com.springer.onix.9783319716558
OTHER EDITION IN ANOTHER MEDIUM
International Standard Book Number
9783319716541
TOPICAL NAME USED AS SUBJECT
Differential equations, Partial.
Geometry, Differential.
Logic, Symbolic and mathematical.
Differential calculus & equations.
Differential equations, Partial.
Geometry, Differential.
Logic, Symbolic and mathematical.
MATHEMATICS-- Calculus.
MATHEMATICS-- Mathematical Analysis.
Maths for computer scientists.
(SUBJECT CATEGORY (Provisional
MAT-- 005000
MAT-- 034000
PBKJ
DEWEY DECIMAL CLASSIFICATION
Number
515/
.
35
Edition
23
LIBRARY OF CONGRESS CLASSIFICATION
Class number
QA377
PERSONAL NAME - PRIMARY RESPONSIBILITY
Krasilʹshchik, I. S., (Iosif Semenovich)
PERSONAL NAME - ALTERNATIVE RESPONSIBILITY
Verbovetsky, Alexander.
Vitolo, Raffaele.
ORIGINATING SOURCE
Date of Transaction
20200823103405.0
Cataloguing Rules (Descriptive Conventions))
pn
ELECTRONIC LOCATION AND ACCESS
Electronic name
مطالعه متن کتاب [Book]
Y
