Bilinear Integrable Systems: from Classical to Quantum, Continuous to Discrete -

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Résumé :
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 ?SHL-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 PAINLEV? 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 H?NON-HEILES HAMILTONIAN.- ON THE BILINEAR FORMS OF PAINLEV?'S 4TH EQUATION....

Sommaire:
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 ?SHL-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 PAINLEV? 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 H?NON-HEILES HAMILTONIAN.- ON THE BILINEAR FORMS OF PAINLEV?'S 4TH EQUATION.