Symmetries and integrability of difference equations

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