Faddeev / Van Moerbeke / Lambert Bilinear Integrable Systems: from Classical to Quantum, Continuous to Discrete

Proceedings of the NATO Advanced Research Workshop on Bilinear Integrable Systems: From Classical to Quantum, Continuous to Discrete St. Petersburg, Russia, 15-19 September 2002
2006
ISBN: 978-1-4020-3503-6
Verlag: Springer Netherland
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 201, 378 Seiten, eBook

Reihe: NATO Science Series II: Mathematics, Physics and Chemistry

The CKP hierarchy and the WDVV prepotential.- Quantum invariance groups of particle algebras.- Algebraic Hirota maps.- Boundary states in Susy Sine-Gordon model.- Geometry of discrete integrability. The consistency approach.- Homoclinic orbits and dressing method.- Riemann-Hilbert problem and algebraic curves.- Analytic and algebraic aspects of Toda field theories and their real Hamiltonian forms.- Bilinear avatars of the discrete Painlevé II equation.- Orthogonal polynomials satisfying Q-difference equations.- Discretization of coupled soliton equations.- An adelic W-algebra and rank one bispectral operators.- Toroidal Lie algebra and bilinear identity of the self-dual Yang-Mills hierarchy.- From soliton equations to their zero curvature formulation.- Covariant forms of Lax one-field operators: from Abelian to non-commutative.- On the Dirichlet boundary problem and Hirota equations.- Functional-difference deformations of Darboux-Pöshl-Teller potentials.- Maxwell equations for quantum space-time.- A solvable model of interacting photons.- Discretization of a Sine-Gordon type equation- Hierarchy of quantum explicitly solvable and integrable models.- A two-parameter elliptic extension of the lattice KDV system.- Travelling waves in a perturbed discrete Sine-Gordon equation.- Quantum VS classical Calogero-Moser systems.- Geometrical dynamics of an integrable piecewise-linear mapping.- Free bosons and dispersionless limit of Hirota tau-function.- Similarity reductions of Hirota bilinear equations and Painlevé equations.- On fundamental cycle of periodic Box-Ball systems.- Combinatorics and integrable geometry.- On reductions of some KDV-type systems and their link to the quartic Hénon-Heiles Hamiltonian.- On the bilinear forms of Painlevés 4th equation.

Zielgruppe

Research

Autoren/Hrsg.

Faddeev, Ludwig

Lambert, Franklin

Van Moerbeke, Pierre

Inhaltsverzeichnis

THE CKP HIERARCHY AND THE WDVV PREPOTENTIAL.- QUANTUM INVARIANCE GROUPS OF PARTICLE ALGEBRAS.- ALGEBRAIC HIROTA MAPS.- BOUNDARY STATES IN SUSY SINE-GORDON MODEL.- GEOMETRY OF DISCRETE INTEGRABILITY. THE CONSISTENCY APPROACH.- HOMOCLINIC ORBITS AND DRESSING METHOD.- RIEMANN-HILBERT PROBLEM AND ALGEBRAIC CURVES.- ANALYTIC AND ALGEBRAIC ASPECTS OF TODA FIELD THEORIES AND THEIR REAL HAMILTONIAN FORMS.- BILINEAR AVATARS OF THE DISCRETE PAINLEV II EQUATION.- ORTHOGONAL POLYNOMIALS SATISFYING Q-DIFFERENCE EQUATIONS.- DISCRETIZATION OF COUPLED SOLITON EQUATIONS.- AN ADELIC W-ALGEBRA AND RANK ONE BISPECTRAL OPERATORS.- TOROIDAL LIE ALGEBRA AND BILINEAR IDENTITY OF THE SELF-DUAL YANG-MILLS HIERARCHY.- FROM SOLITON EQUATIONS TO THEIR ZERO CURVATURE FORMULATION.- COVARIANT FORMS OF LAX ONE-FIELD OPERATORS: FROM ABELIAN TO NONCOMMUTATIVE.- ON THE DIRICHLET BOUNDARY PROBLEM AND HIROTA EQUATIONS.- FUNCTIONAL-DIFFERENCE DEFORMATIONS OF DARBOUX-P ÖSHL-TELLER POTENTIALS.- MAXWELL EQUATIONS FOR QUANTUM SPACE-TIME.- A SOLVABLE MODEL OF INTERACTING PHOTONS.- DISCRETIZATION OF A SINE-GORDON TYPE EQUATION.- HIERARCHY OF QUANTUM EXPLICITLY SOLVABLE AND INTEGRABLE MODELS.- A TWO-PARAMETER ELLIPTIC EXTENSION OF THE LATTICE KdV SYSTEM.- TRAVELLINGWAVES IN A PERTURBED DISCRETE SINE-GORDON EQUATION.- QUANTUM VS CLASSICAL CALOGERO–MOSER SYSTEMS.- GEOMETRICAL DYNAMICS OF AN INTEGRABLE PIECEWISE-LINEAR MAPPING.- FREE BOSONS AND DISPERSIONLESS LIMIT OF HIROTA TAU-FUNCTION.- SIMILARITY REDUCTIONS OF HIROTA BILINEAR EQUATIONS AND PAINLEVÉ EQUATIONS.- ON FUNDAMENTAL CYCLE OF PERIODIC BOX-BALL SYSTEMS.- COMBINATORICS AND INTEGRABLE GEOMETRY.- ON REDUCTIONS OF SOME KdV-TYPE SYSTEMS AND THEIR LINK TO THE QUARTIC HÉNON-HEILES HAMILTONIAN.- ON THE BILINEAR FORMS OF PAINLEVé'S 4TH EQUATION.