The symbolic computation of integrability structures for partial differential equations / Joseph Krasil'shchik, Alexander Verbovetsky, Raffaele Vitolo

• Record Nr.: UNISALENTO991003589739707536
• Autore: Krasilʹshchik, Iosif Semenovich
• ISBN: 9783319716541
• Descrizione fisica: xv, 263 p. ; 24 cm
• Collana: Texts and monographs in symbolic computation
• Classificazione: AMS 68-02; AMS 35A30
• Altri autori (Persone): Verbovetsky, Alexanderauthor; Vitolo, Raffaeleauthor
• Disciplina: 515.353
• Soggetti: Computer Science; Differential equations, Partial; Logic, Symbolic and mathematical; Geometry, Differential
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di contenuto: 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 Theory4.1.1 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