The symbolic computation of integrability structures for partial differential equations. ([2017])

• Record Type: Book
• Further Information: Note: Joseph Krasil'shchik, Alexander Verbovetsky, Raffaele Vitolo.
• Other Names: Krasilʹshchik, I. S (Iosif Semenovich); Verbovetsky, Alexander; Vitolo, Raffaele
• 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
• Publisher Details: Cham : Springer
• Publication Date: 2017
• Extent: 1 online resource
• Subjects: 515/.35; Mathematics; Differential equations, Partial; Logic, Symbolic and mathematical; Geometry, Differential; MATHEMATICS / Calculus; MATHEMATICS / Mathematical Analysis; Differential equations, Partial; Geometry, Differential; Logic, Symbolic and mathematical; Computers -- Data Processing; Maths for computer scientists; Functional equations; Computer science; Algebra -- Data processing; Mathematics -- Mathematical Analysis; Differential calculus & equations; Electronic books
• Languages: English
• ISBNs: 9783319716558; 3319716557
• Related ISBNs: 9783319716541
• Notes: Note: Online resource; title from PDF title page (EBSCO, viewed April 10, 2018)
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.