Bilinear Integrable Systems: From Classical to Quantum, Continuous to Discrete

✍ Scribed by Henrik Aratyn, Johan Van de Leur (auth.), Ludwig Faddeev, Pierre Van Moerbeke, Franklin Lambert (eds.)

• Publisher: Springer Netherlands
• Year: 2006
• Tongue: English
• Leaves: 393
• Series: NATO Science Series 201
• Edition: 1
• Category: Library

✦ Synopsis

The CKP hierarchy and the WDVV prepotential; H. Aratyn, J. van de Leur.- Quantum invariance groups of particle algebras; M. Arik.- Algebraic Hirota maps; C. Athorne.- Boundary states in Susy Sine-Gordon model; Z. Bajnok et al.- Geometry of discrete integrability. The consistency approach; A.I. Bobenko.- Homoclinic orbits and dressing method; E.V. Doktorov, V.M. Rothos.- Riemann-Hilbert problem and algebraic curves; V. Enolskii, T. Grava.- Analytic and algebraic aspects of Toda field theories and their real Hamiltonian forms; V.S. Gerdjikov.- Bilinear avatars of the discrete Painlevé II equation; B. Grammaticos et al.- Orthogonal polynomials satisfying Q-difference equations; L. Haine.- Discretization of coupled soliton equations; R. Hirota.- An adelic W-algebra and rank one bispectral operators; E. Horozov.- Toroidal Lie algebra and bilinear identity of the self-dual Yang-Mills hierarchy; S. Kakei.- From soliton equations to their zero curvature formulation; F. Lambert, J. Springael.- Covariant forms of Lax one-field operators: from Abelian to non-commutative; S. Leble.- On the Dirichlet boundary problem and Hirota equations; A. Marshakov, A. Zabrodin.- Functional-difference deformations of Darboux-Pöshl-Teller potentials; V.B. Matveev.- Maxwell equations for quantum space-time; R.M. Mir-Kasmov.- A solvable model of interacting photons; J. Naudts.- Discretization of a Sine-Gordon type equation; Y. Ohta.- Hierarchy of quantum explicitly solvable and integrable models; A.K. Pogrebkov.- A two-parameter elliptic extension of the lattice KDV system; S.E. Puttock, F.W. Nijhoff.- Travelling waves in a per-turbed discrete Sine-Gordon equation; V.M. Rothos, M. Feckan.- Quantum VS classical Calogero-Moser systems; R. Sasaki.- Geometrical dynamics of an integrable piecewise-linear mapping; D. Takahashi, M. Iwao.- Free bosons and dispersionless limit of Hirota tau-function; L.A. Takhtajan.- Similarity reductions of Hirota bilinear equations and Painlevé equations; K.M. Tamizhmani et al.- On fundamental cycle of periodic Box-Ball systems; T. Tokihiro.- Combinatorics and integrable geometry; P. van Moerbeke.- On reductions of some KDV-type systems and their link to the quartic Hénon-Heiles Hamiltonian; C. Verhoeven et al.- On the bilinear forms of Painlevé’s 4th equation; R. Willox, J. Hietarinta.

✦ Table of Contents

Front Matter....Pages I-XVII
THE CKP HIERARCHY AND THE WDVV PREPOTENTIAL....Pages 1-11
QUANTUM INVARIANCE GROUPS OF PARTICLE ALGEBRAS....Pages 13-16
ALGEBRAIC HIROTA MAPS....Pages 17-33
BOUNDARY STATES IN SUSY SINE-GORDON MODEL....Pages 35-42
GEOMETRY OF DISCRETE INTEGRABILITY. THE CONSISTENCY APPROACH....Pages 43-53
HOMOCLINIC ORBITS AND DRESSING METHOD....Pages 55-64
RIEMANN-HILBERT PROBLEM AND ALGEBRAIC CURVES....Pages 65-76
ANALYTIC AND ALGEBRAIC ASPECTS OF TODA FIELD THEORIES AND THEIR REAL HAMILTONIAN FORMS....Pages 77-83
BILINEAR AVATARS OF THE DISCRETE PAINLEV II EQUATION....Pages 85-96
ORTHOGONAL POLYNOMIALS SATISFYING Q-DIFFERENCE EQUATIONS....Pages 97-112
DISCRETIZATION OF COUPLED SOLITON EQUATIONS....Pages 113-122
AN ADELIC W-ALGEBRA AND RANK ONE BISPECTRAL OPERATORS....Pages 123-136
TOROIDAL LIE ALGEBRA AND BILINEAR IDENTITY OF THE SELF-DUAL YANG-MILLS HIERARCHY....Pages 137-146
FROM SOLITON EQUATIONS TO THEIR ZERO CURVATURE FORMULATION....Pages 147-159
COVARIANT FORMS OF LAX ONE-FIELD OPERATORS: FROM ABELIAN TO NONCOMMUTATIVE....Pages 161-173
ON THE DIRICHLET BOUNDARY PROBLEM AND HIROTA EQUATIONS....Pages 175-190
FUNCTIONAL-DIFFERENCE DEFORMATIONS OF DARBOUX-P ÖSHL-TELLER POTENTIALS....Pages 191-208
MAXWELL EQUATIONS FOR QUANTUM SPACE-TIME....Pages 209-217
A SOLVABLE MODEL OF INTERACTING PHOTONS....Pages 219-224
DISCRETIZATION OF A SINE-GORDON TYPE EQUATION....Pages 225-230
HIERARCHY OF QUANTUM EXPLICITLY SOLVABLE AND INTEGRABLE MODELS....Pages 231-244
A TWO-PARAMETER ELLIPTIC EXTENSION OF THE LATTICE KdV SYSTEM....Pages 245-251
TRAVELLINGWAVES IN A PERTURBED DISCRETE SINE-GORDON EQUATION....Pages 253-257
QUANTUM VS CLASSICAL CALOGERO–MOSER SYSTEMS....Pages 259-289
GEOMETRICAL DYNAMICS OF AN INTEGRABLE PIECEWISE-LINEAR MAPPING....Pages 291-300
FREE BOSONS AND DISPERSIONLESS LIMIT OF HIROTA TAU-FUNCTION....Pages 301-311
SIMILARITY REDUCTIONS OF HIROTA BILINEAR EQUATIONS AND PAINLEVÉ EQUATIONS....Pages 313-323
ON FUNDAMENTAL CYCLE OF PERIODIC BOX-BALL SYSTEMS....Pages 325-334
COMBINATORICS AND INTEGRABLE GEOMETRY....Pages 335-362
ON REDUCTIONS OF SOME KdV-TYPE SYSTEMS AND THEIR LINK TO THE QUARTIC HÉNON-HEILES HAMILTONIAN....Pages 363-374
ON THE BILINEAR FORMS OF PAINLEVé'S 4TH EQUATION....Pages 375-390

✦ Subjects

Mathematical Methods in Physics