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Analytic-Bilinear Approach to Integrable Hierarchies

BuchKartoniert, Paperback
267 Seiten
Englisch
Springer Netherlandserschienen am10.10.2012Softcover reprint of the original 1st ed. 1999
The language of the a-dressing method is suitable for applications to integrable nonlinear PDEs, integrable nonlinear discrete equations, and, as recently discovered, for t.he applications of integrable systems to continuous and discret.e geometry.mehr
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Produkt

KlappentextThe language of the a-dressing method is suitable for applications to integrable nonlinear PDEs, integrable nonlinear discrete equations, and, as recently discovered, for t.he applications of integrable systems to continuous and discret.e geometry.
Details
ISBN/GTIN978-94-010-5922-0
ProduktartBuch
EinbandartKartoniert, Paperback
Erscheinungsjahr2012
Erscheinungsdatum10.10.2012
AuflageSoftcover reprint of the original 1st ed. 1999
ReiheMathematics and Its Applications
Seiten267 Seiten
SpracheEnglisch
Gewicht459 g
IllustrationenXII, 267 p.
Artikel-Nr.30370876

Inhalt/Kritik

Inhaltsverzeichnis
1 Introduction.- 1.1 Hirota Bilinear Identity.- 1.2 Meromorphic Loops, Determinant Formula and the ?-Function.- 1.3 Integrable Discrete Equations.- 1.4 From Discrete Equations to the Continuous Hierarchy.- 2 Hirota Bilinear Identity for the Cauchy Kernel.- 2.1 Boundary Problems for the ¯?-Operator in the Unit Disc.- 2.2 General Boundary Problems with Zero Index.- 2.3 Rational Deformations of the Boundary Problems.- 2.4 Hirota Bilinear Identity.- 2.5 Determinant Formula for Action of Meromorphic Loops on the Cauchy Kernel.- 2.6 ?-Function for the One-Component Case.- 3 Rational Loops and Integrable Discrete Equations. I: Zero Local Indices.- 3.1 One-Component Case.- 3.2 General Matrix Equations for the Multicomponent Case.- 4 Rational Loops and Integrable Discrete Equations. II: Two-Component Case.- 4.1 DS case.- 4.2 2DTL Case.- 5 Rational Loops and Integrable Discrete Equations. III: The General Case.- 5.1 General Multicomponent Case.- 5.2 ?-Function for the Multicomponent Case.- 5.3 Three-Component Case.- 5.4 Four-Component Case.- 5.5 Five-Component and Six-Component Cases.- 6 Generalized KP Hierarchy.- 6.1 Generalized Hirota Identity from the ¯?-Dressing Method.- 6.2 The Generalized KP Hierarchy.- 6.3 KP Hierarchy in the Moving Frame´. Darboux Equations as the Horizontal Subhierarchy.- 6.4 Combescure Symmetry Transformations.- 6.5 ?-Function and Addition Formulae.- 6.6 ?-Function as a Functional.- 6.7 From the Discrete Case to the Continuous.- 7 Multicomponent Kp Hierarchy.- 7.1 Multicomponent Case with Zero Local Indices.- 7.2 ?-Function and Closed 1-Form for ?+N.- 7.3 Generalized DS Hierarchy.- 7.4 Loop Group ? and 2DTL Hierarchy.- 8 On The ¯?-Dressing Method.- 8.1 General Scheme.- 8.2 Matrix Lattice and q-Difference Darboux Equations.- 8.3 Special Cases of Nonlocal ¯?-Problem.- 8.4 On Some Equations, Integrable Via ¯?-Dressing Method.- 8.5 Solutions with Special Properties.- 8.6 Boussinesq Equation.- 8.7 Relativistically-Invariant Systems.- 8.8 Inverse Problems for the Differential Operator of Arbitrary Order on the Line.mehr