LEADER 04551nam a2200421 i 4500 001 991003589739707536 008 190110s2017 sz o 000 0 eng d 020 $a9783319716541 035 $ab14356685-39ule_inst 040 $aBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematica$beng 082 04$a515.353$222 084 $aAMS 68-02 084 $aAMS 35A30 100 1 $aKrasil?shchik, Iosif Semenovich$0350820 245 14$aThe symbolic computation of integrability structures for partial differential equations /$cJoseph Krasil'shchik, Alexander Verbovetsky, Raffaele Vitolo 264 1$aCham :$bSpringer,$c[2017] 300 $axv, 263 p. ;$c24 cm 336 $atext$btxt$2rdacontent 337 $aunmediated$bn$2rdamedia 338 $avolume$bnc$2rdacarrier 490 1 $aTexts and monographs in symbolic computation 505 0 $aIntro; 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 505 8 $a2.3.1 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 505 8 $a4.1 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 505 8 $a5.2.1 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 505 8 $a7.1.2 Hereditary Operators7.1.3 Recursion Operators as Bäcklund Transformations; 7.2 Examples; 7.2.1 Korteweg-de Vries Equation; 7.2.2 Dispersionless Boussinesq System; 7.2.3 Camassa-Holm Equation; 7.2.4 Heat Equation; 7.2.5 Multi-dimensional Examples; 7.2.5.1 The Plebanski Equation; 7.2.5.2 The rdDym Equation; 7.2.5.3 The Pavlov Equation; 7.2.5.4 The Universal Hierarchy Equation; 8 Variational Symplectic Structures; 8.1 General Theory; 8.2 Examples; 8.2.1 The Two-Dimensional WDVV Equation; 8.2.2 The Krichever-Novikov Equation; 8.2.3 Korteweg-de Vries Equation 650 0$aComputer Science 650 0$aDifferential equations, Partial 650 0$aLogic, Symbolic and mathematical 650 0$aGeometry, Differential 700 1 $aVerbovetsky, Alexander$eauthor$4http://id.loc.gov/vocabulary/relators/aut$0734431 700 1 $aVitolo, Raffaele$eauthor$4http://id.loc.gov/vocabulary/relators/aut$0785785 907 $a.b14356685$b01-02-19$c10-01-19 912 $a991003589739707536 945 $aLE013 68-XX KRA11 (2017)$g1$i2013000296609$lle013$og$pE98.79$q-$rl$s- $t0$u0$v0$w0$x0$y.i15875611$z01-02-19 996 $aSymbolic computation of integrability structures for partial differential equations$91749481 997 $aUNISALENTO 998 $ale013$b10-01-19$cm$da $e-$feng$gsz $h4$i0