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Symmetries and Integrability of Difference Equations

About this Title

Decio Levi, University of Rome III, Rome, Italy, Luc Vinet, University of Montreal, Montreal, QC, Canada and Pavel Winternitz, University of Montreal, Montreal, QC, Canada, Editors

Publication: CRM Proceedings and Lecture Notes
Publication Year: 1996; Volume 9
ISBNs: 978-0-8218-0601-2 (print); 978-1-4704-3923-1 (online)
DOI: https://doi.org/10.1090/crmp/009
MathSciNet review: MR1416820
MSC: Primary 39-06; Secondary 00B25, 33-06

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Table of Contents

Front/Back Matter

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Chapters

• On the numerics of integrable discretizations
• A brief introduction to the world of $q$
• A Ramanujan-type for the Al-Salam and Ismail biorthogonal rational functions
• Knizhnik-Zamolodchikov equations and the algebraic Bethe Ansatz
• Integrable quantum mappings
• Local master symmetries of differential-difference equations
• Bäcklund transformations and hierarchies of exact solutions for the fourth Painlevé equation and their application to discrete equations
• On the diagonalization of difference Calogero-Sutherland systems
• The integrable dynamics of a discrete curve
• Continuous symmetries of finite-difference evolution equations and grids
• Basic Bessel functions and $q$-difference equations
• Difference equations and gauge symmetry
• An operator-valued Riemann-Hilbert problem associated with the XXX model
• Orthogonal polynomials satisfying differential equations: The role of the Darboux transformation
• Quantum isomonodromic deformations and the Knizhnik-Zamolodchikov equations
• Lie symmetries and linearizations of analytic discrete dynamical systems
• $q$-algebra representations of the Euclidean, pseudo-Euclidean, and oscillator algebras, and their tensor products
• $_3F_2$(1) hypergeometric function and quadratic $R$-matrix algebra
• Lie point symmetries of differential difference equations
• The factorization method for the differential-difference relativistic Schrödinger equation and $q$-deformations
• Quantum deformations of $\tau $-functions, bilinear identities, and representation theory
• The factorization method and hierarchies of $q$-oscillator Hamiltonians
• Discrete-time Calogero-Moser model and lattice KP equations
• Bilinear structure and exact solutions of the discrete Painlevé I equation
• Integrable difference equations and numerical analysis algorithms
• An integral representation of the very-well-poised $_{8{\psi }8}$
• Singular analogue of the Fourier transformation for the Askey-Wilson polynomials
• Singularity confinement
• Recurrence relation approach for connection coefficients. Applications to classical discrete orthogonal polynomials
• Linearisation of difference equations using factorisable Lie symmetries
• First integrals of the infinite Toda lattice
• Non semisimple quantum groups and “exponential mappings”
• Discrete Schrödinger equation, Darboux transformations, and orthogonal polynomials
• Integrable cellular automata and AKNS hierarchy
• On some rational Coxeter groups

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