| Document Type
|
:
|
BL
|
| Record Number
|
:
|
864285
|
| Main Entry
|
:
|
Krasilʹshchik, I. S., (Iosif Semenovich)
|
| Title & Author
|
:
|
The symbolic computation of integrability structures for partial differential equations /\ Joseph Krasil'shchik, Alexander Verbovetsky, Raffaele Vitolo.
|
| Publication Statement
|
:
|
Cham :: Springer,, [2017]
|
| Series Statement
|
:
|
Texts and monographs in symbolic computation
|
| Page. NO
|
:
|
1 online resource
|
| ISBN
|
:
|
3319716549
|
|
|
:
|
: 3319716557
|
|
|
:
|
: 9783319716541
|
|
|
:
|
: 9783319716558
|
|
|
:
|
9783319716541
|
| Contents
|
:
|
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
|
|
|
:
|
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
|
|
|
:
|
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
|
|
|
:
|
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
|
|
|
:
|
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
|
| 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 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.
|
| Subject
|
:
|
Differential equations, Partial.
|
| Subject
|
:
|
Geometry, Differential.
|
| Subject
|
:
|
Logic, Symbolic and mathematical.
|
| Subject
|
:
|
Differential calculus equations.
|
| Subject
|
:
|
Differential equations, Partial.
|
| Subject
|
:
|
Geometry, Differential.
|
| Subject
|
:
|
Logic, Symbolic and mathematical.
|
| Subject
|
:
|
MATHEMATICS-- Calculus.
|
| Subject
|
:
|
MATHEMATICS-- Mathematical Analysis.
|
| Subject
|
:
|
Maths for computer scientists.
|
| Dewey Classification
|
:
|
515/.35
|
| LC Classification
|
:
|
QA377
|
| Added Entry
|
:
|
Verbovetsky, Alexander.
|
|
|
:
|
Vitolo, Raffaele.
|