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Symmetries and Integrability of Difference Equations : London Mathematical Society Lecture Notes - Peter A. Clarkson

Symmetries and Integrability of Difference Equations

London Mathematical Society Lecture Notes

By: Peter A. Clarkson (Editor), Frank W. Nijhoff (Editor), N. J. Hitchin (Editor)

Paperback Published: 5th April 1999
ISBN: 9780521596992
Number Of Pages: 444

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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.

'... this book will form an inspiration for further research and so help to establish the links between the various communities working on discrete systems.' European Mathematical Society

Partial Differential Equations
Discrete linearisable Gambier equations A. K. Common,
Generalized Bäcklund transformation and new explicit solutions of the two-dimensional Toda equation
Different aspects of relativistic Toda Chain
Integrable Mappings
Integrable symplectic maps
An iterative process on quartics and integrable symplectic maps
Integrable mappings of KdV type and hyperelliptic addition theorems
R-matrix hierarchies, integrable lattice systems and their integrable discretizations
Discrete Geometry
Discrete conformal maps and surfaces
The Bäcklund transformation for discrete isothermic surfaces
Integrable discrete geometry with ruler and compass
Self-dual Einstein spaces and a discrete Tzitzeica equation. A permutability theorem link
Asymptotic Analysis
New solutions of the non-stationary Schrödinger and Kadomtsev-Petviashvili equation
On asymptotic analysis of the orthogonal polynomials via the Riemann-Hilbert method
A new spectral transform for solving the continuous and spatially discrete heat equation on simple trees
Discrete Painlevé Equations
The discrete Painlevé hierarchy
Rational solutions to d-PIV
The discrete Painlevé II equation and the classical special functions
Freud's equations for orthogonal polynomials as discrete Painlevé equations
Symmetries of Difference Equations
An approach to master symmetries of lattice equations
Symmetries and generalized symmetries for discrete dynamical systems
Nonlinear difference equations with superposition formulas
Numerical Methods and Miscellaneous
Generalising the Painlevé truncation: expansions in Riccati pseudopotentials
Symplectic Runge-Kutta schemes
Cellular Automata
Soliton cellular automata
Painlevé equations and cellular automata
2+1 Dimensional soliton cellular automaton
q-Special Functions and q-Difference Equations
Fourier-Gauss transforms of q-exponential and q-Bessel functions
The Wilson bispectral involution: some elementary examples
Factorisation of Macdonald polynomials
Local Yang-Baxter relations associated with Hirota's discrete equation
Ultra-discrete soliton systems
Schrödinger equation on quantum homogeneous spaces
Some algebraic solutions of discrete equations from anticommuting variables
Q-combinatorics and quantum integrability
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521596992
ISBN-10: 0521596998
Series: London Mathematical Society Lecture Notes
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 444
Published: 5th April 1999
Publisher: CAMBRIDGE UNIV PR
Country of Publication: GB
Dimensions (cm): 22.86 x 15.24  x 2.52
Weight (kg): 0.65