Titlebook: Bilinear Integrable Systems: from Classical to Quantum, Continuous to Discrete; Proceedings of the N Ludwig Faddeev,Pierre Van Moerbeke,Fra

省略

BOUNDARY STATES IN SUSY SINE-GORDON MODEL,After reviewing briefly the basic concepts and problems of boundary integrable theories we outline a boostrap solution leading to the spectrum of boundary states in SUSY sine-Gordon model with supersymmetric integrable boundary condition.

Lignans

GEOMETRY OF DISCRETE INTEGRABILITY. THE CONSISTENCY APPROACH,Long before the theory of solitons, geometers used integrable equations to describe various special curves, surfaces etc. At that time no relation to mathematical physics was known, and quite different geometries appeared in this context (we will call them integrable) were unified by their common geometric features:

豐富

ORTHOGONAL POLYNOMIALS SATISFYING Q-DIFFERENCE EQUATIONS,The Askey–Wilson polynomials are the most general orthogonal polynomials, which are eigenfunctions of a second order q-difference operator. I survey recent results aiming at constructing all orthogonal polynomials which are eigenfunctions of a q-difference operator of an arbitrary order, by means of the lattice Darboux transformation.

Accede

DISCRETIZATION OF COUPLED SOLITON EQUATIONS,We describe integrable discretization of coupled forms of the well-known soliton equations such as KdV equation, modified KdV equation, sine-Gordon equation and nonlinear Schr?dinger equation.

cogitate

TOROIDAL LIE ALGEBRA AND BILINEAR IDENTITY OF THE SELF-DUAL YANG-MILLS HIERARCHY,Bilinear identity associated with the self-dual Yang-Mills hierarchy is discussed by using a fermionic representation of the toroidal Lie algebra . . ..

牙齒

ALGEBRAIC HIROTA MAPS,ralized) Hirota derivatives in the limit of the dimension of the representation becoming infinite and we discuss an application to the theory of -functions associated with hyperelliptic curves of genus 2.

Abutment

ANALYTIC AND ALGEBRAIC ASPECTS OF TODA FIELD THEORIES AND THEIR REAL HAMILTONIAN FORMS,anced the development of graded and Kac-Moody algebras and the method of reductions in the inverse scattering method. Here we outline the basic ideas and some of their latest developments which allowed to relate to each TFT a family of its real Hamiltonian forms.

botany

松軟無(wú)力

AN ADELIC W-ALGEBRA AND RANK ONE BISPECTRAL OPERATORS,ine with rational coefficients. We construct its natural bosonic representation similar to highest weight representation. Then we show that the rank one algebras of bispectral operators are in 1:1 correspondence with the tau-functions in this representation.

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