Symmetries and integrability of difference equations ; [The second International Conference on "Symmetries and Integrability of Difference Equations" (SIDE II) was held at the University of Kent at Canterbury, July 1-5, 1996

There Has In Recent Years Been A Remarkable Growth Of Interest In The Area Of Discrete Integrable Systems. Much Progress Has Been Made By Applying Symmetry Groups To The Study Of Differential Equations, And Connections Have Been Made To Other Topics Such As Numerical Methods, Cellular Automata And Mathematical Physics. This Volume Comprises State Of The Art Articles From Almost All The Leading Workers In This Important And Rapidly Developing Area, Making It A Necessary Resource For All Researchers Interested In Discrete Integrable Systems Or Related Subjects. 1. Partial Difference Equations. Discrete Linearisable Gambier Equations / A.k. Common, E. Hesameddini And M. Musette. Generalized Backlund Transformation And New Explicit Solutions Of The Two-dimensional Toda Equation / X.-b. Hu And P.a. Clarkson. Different Aspects Of Relativistic Toda Chain / S. Kharchev, A. Mironov And A. Zhedanov -- 2. Integrable Mappings. Integrable Symplectic Maps / A.p. Fordy. An Iterative Process On Quartics And Integrable Symplectic Maps / J.p. Francoise And O. Ragnisco. Integrable Mappings Of Kdv Type And Hyperelliptic Addition Formulae / F.w. Nijhoff And V.z. Enolskii. R-matrix Hierarchies, Integrable Lattice Systems And Their Integrable Discretizations / Yu. B. Suris -- 3. Discrete Geometry. Edited By Peter A. Clarkson, Frank W. Nijhoff. Second International Conference ... Held At The University Of Kent At Canterbury, July 1-5, 1996--pref. Includes Bibliographical References. Cover......Page 1 Symmetries and Integrability of Difference Equations......Page 4 ISBN 0521596998 ISBN......Page 5 Contents......Page 6 Preface......Page 10 List of Participants......Page 16 1 Partial Difference Equations......Page 18 Discrete linearisable Gambier equations......Page 20 Generalized Backlund transformation and new explicit solutions of the two-dimensional Toda equation......Page 32 Different aspects of relativistic Toda chain......Page 40 2 Integrable Mappings......Page 58 Integrable symplectic maps......Page 60 An iterative process on quartics and integrable symplectic maps......Page 73 Integrable mappings of KdV type and hyperelliptic addition formulae......Page 81 R-matrix hierarchies, integrable lattice systems and their integrable discretizations......Page 96 3 Discrete Geometry......Page 112 Discrete conformal maps and surfaces......Page 114 The Backlund transformation for discrete isothermic surfaces......Page 126 Integrable discrete geometry with ruler and compass......Page 139 Self-dual Einstein spaces and a discrete Tzitzeica equation, a permutability theorem link......Page 154 4 Asymptotic Analysis......Page 166 New solutions of nonstationary Schrodinger and Kadomtsev-Petviashvili equations......Page 168 On asymptotic analysis of orthogonal polynomials via the Riemann-Hilbert method......Page 182 A new spectral transform for solving the continuous and spatially discrete heat equations on simple trees......Page 195 5 Discrete Painlevé Equations......Page 212 The discrete Painlevé I hierarchy......Page 214 Rational solutions to dPIV......Page 223 The discrete Painleve II equation and the classical special functions......Page 234 Freud's equations for orthogonal polynomials as discrete Painleve equations......Page 245 6 Symmetries of Difference Equations......Page 262 An approach to master symmetries of lattice equations......Page 264 Symmetries and generalized symmetries for discrete dynamical systems......Page 278 Nonlinear difference equations with superposition formulae......Page 292 7 Numerical Methods and Miscellaneous......Page 302 Generalised Painleve truncation: expansion in Riccati pseudopotentials......Page 304 Symplectic Runge-Kutta schemes......Page 316 8 Cellular Automata......Page 328 Soliton Cellular Automata......Page 330 Painleve equations and cellular automata......Page 342 Soliton cellular automaton......Page 351 9 q-Special Functions and q-Difference Equations......Page 360 Fourier-Gauss transform of some q-special functions......Page 362 The Wilson bispectral involution: some elementary examples......Page 370 Factorisation of Macdonald polynomials......Page 387 10 Quantum Aspects and Yang-Baxter Equations......Page 402 Schrödinger equation on quantum homogeneous spaces......Page 404 Local Yang-Baxter relations associated with Hirota's discrete equation......Page 419 Some algebraic solutions of discrete equations from anticommuting variables......Page 427 q-combinatorics and quantum integrability......Page 437