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Softcover ISBN:  9780821821282 
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Softcover ISBN:  9780821821282 
Product Code:  CRMP/25 
List Price:  $123.00 
MAA Member Price:  $110.70 
AMS Member Price:  $98.40 
eBook ISBN:  9781470439392 
Product Code:  CRMP/25.E 
List Price:  $120.00 
MAA Member Price:  $108.00 
AMS Member Price:  $96.00 
Softcover ISBN:  9780821821282 
eBook ISBN:  9781470439392 
Product Code:  CRMP/25.B 
List Price:  $243.00 $183.00 
MAA Member Price:  $218.70 $164.70 
AMS Member Price:  $194.40 $146.40 

Book DetailsCRM Proceedings & Lecture NotesVolume: 25; 2000; 444 ppMSC: Primary 22; 33; 42; 39; 53
This volume contains the proceedings of the third meeting on “Symmetries and Integrability of Difference Equations” (SIDE III). The collection includes original results not published elsewhere and articles that give a rigorous but concise overview of their subject, and provides a complete description of the state of the art. Research in the field of difference equations—often referred to more generally as discrete systems—has undergone impressive development in recent years. In this collection the reader finds the most important new developments in a number of areas, including: Lietype symmetries of differentialdifference and differencedifference equations, integrability of fully discrete systems such as cellular automata, the connection between integrability and discrete geometry, the isomonodromy approach to discrete spectral problems and related discrete Painlevé equations, difference and qdifference equations and orthogonal polynomials, difference equations and quantum groups, and integrability and chaos in discretetime dynamical systems.
The proceedings will be valuable to mathematicians and theoretical physicists interested in the mathematical aspects and/or in the physical applications of discrete nonlinear dynamics, with special emphasis on the systems that can be integrated by analytic methods or at least admit special explicit solutions. The research in this volume will also be of interest to engineers working in discrete dynamics as well as to theoretical biologists and economists.
Titles in this series are copublished with the Centre de Recherches Mathématiques.
ReadershipGraduate students in mathematics and theoretical physics; researchers in mathematics, physics and informatics.

Table of Contents

Chapters

Billiard weak solutions of nonlinear PDE’s and Toda flows

FourierGauss transforms of some $q$spectral functions

Integrable differentialdifference systems in (2 + 1)dimensions and their Hamiltonian structure

Möbius invariant integrable lattice equations associated with the generalized KP hierarchy

Wave soliton solutions on a generic background for KPI equation

Difference and differential equations and convergence acceleration algorithms

On the dynamics of rational solutions for 1D Volterra system

Monodromy data for the discrete first Painlevé hierarchy

Differential identities, generalized polynomials and applications in physics and mathematics

Lattice geometry of the Hirota equation

Integrable discrete geometry: The quadrilateral lattice, its transformations and reductions

On the Kleinian construction of abelian functions of canonical algebraic curves

Discrete equations and the singular manifold method

Discrete versions of some algebraic integrable systems related to generalized Jacobians

New potential symmetries

Symmetry classification of systems of differentialdifference equations

Integrable boundary conditions for nonlinear lattices

Modular invariants and generalized Halphen systems

Symmetry preserving discretization of the Burgers equation

Singularity confinement and degree growth

Timediscretization of soliton equations

Bäcklund transformations for the HénonHeiles and Garnier systems

Irregular singular behaviour in the first discrete Painlevé equation

Rational and special solutions of the $P_{\mathrm {II}}$ hierarchy

Linearisable systems and the Gambier approach

Difference equations of PoincaréPerron type and central twopoint connection problems

Selfsimilarity in spectral problems and $q$special functions

Lie point symmetries of discrete and continual SU($\infty $) Toda field theory

A note on integrable systems related to discrete time Toda lattice

The integral formula for the solutions of the quantum KnizhnikZamolodchikov equation associated with $U_q(\widehat {sl}_n)$ for $q = 1$

Symmetries of the discrete Schrödinger equation and its quantum deformations

Determinant and Pfaffian solutions for discrete soliton equations

Difference isomonodromy problems and discrete Painlevé equations

Discrete equations of motion for $A_{k1}$ algebra

Discrete Painlevé equations from nonisospectral soliton equations

A study of the continuous and discrete Gambier systems

Discrete surfaces of revolution

KacMoodyVirasoro algebras and integrability of certain higher dimensional nonlinear evolutionary equations

Different faces of harmonic oscillator

Nonsymmetric linear difference equations for multiple orthogonal polynomials

Asymptotics for solution to the Cauchy problem for Volterra lattice with steplike initial values

Complexity and integrability


Reviews

Strongly recommend this volume to all libraries of research institutions and to mathematicians with interest in difference equations.
CMS Notes


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This volume contains the proceedings of the third meeting on “Symmetries and Integrability of Difference Equations” (SIDE III). The collection includes original results not published elsewhere and articles that give a rigorous but concise overview of their subject, and provides a complete description of the state of the art. Research in the field of difference equations—often referred to more generally as discrete systems—has undergone impressive development in recent years. In this collection the reader finds the most important new developments in a number of areas, including: Lietype symmetries of differentialdifference and differencedifference equations, integrability of fully discrete systems such as cellular automata, the connection between integrability and discrete geometry, the isomonodromy approach to discrete spectral problems and related discrete Painlevé equations, difference and qdifference equations and orthogonal polynomials, difference equations and quantum groups, and integrability and chaos in discretetime dynamical systems.
The proceedings will be valuable to mathematicians and theoretical physicists interested in the mathematical aspects and/or in the physical applications of discrete nonlinear dynamics, with special emphasis on the systems that can be integrated by analytic methods or at least admit special explicit solutions. The research in this volume will also be of interest to engineers working in discrete dynamics as well as to theoretical biologists and economists.
Titles in this series are copublished with the Centre de Recherches Mathématiques.
Graduate students in mathematics and theoretical physics; researchers in mathematics, physics and informatics.

Chapters

Billiard weak solutions of nonlinear PDE’s and Toda flows

FourierGauss transforms of some $q$spectral functions

Integrable differentialdifference systems in (2 + 1)dimensions and their Hamiltonian structure

Möbius invariant integrable lattice equations associated with the generalized KP hierarchy

Wave soliton solutions on a generic background for KPI equation

Difference and differential equations and convergence acceleration algorithms

On the dynamics of rational solutions for 1D Volterra system

Monodromy data for the discrete first Painlevé hierarchy

Differential identities, generalized polynomials and applications in physics and mathematics

Lattice geometry of the Hirota equation

Integrable discrete geometry: The quadrilateral lattice, its transformations and reductions

On the Kleinian construction of abelian functions of canonical algebraic curves

Discrete equations and the singular manifold method

Discrete versions of some algebraic integrable systems related to generalized Jacobians

New potential symmetries

Symmetry classification of systems of differentialdifference equations

Integrable boundary conditions for nonlinear lattices

Modular invariants and generalized Halphen systems

Symmetry preserving discretization of the Burgers equation

Singularity confinement and degree growth

Timediscretization of soliton equations

Bäcklund transformations for the HénonHeiles and Garnier systems

Irregular singular behaviour in the first discrete Painlevé equation

Rational and special solutions of the $P_{\mathrm {II}}$ hierarchy

Linearisable systems and the Gambier approach

Difference equations of PoincaréPerron type and central twopoint connection problems

Selfsimilarity in spectral problems and $q$special functions

Lie point symmetries of discrete and continual SU($\infty $) Toda field theory

A note on integrable systems related to discrete time Toda lattice

The integral formula for the solutions of the quantum KnizhnikZamolodchikov equation associated with $U_q(\widehat {sl}_n)$ for $q = 1$

Symmetries of the discrete Schrödinger equation and its quantum deformations

Determinant and Pfaffian solutions for discrete soliton equations

Difference isomonodromy problems and discrete Painlevé equations

Discrete equations of motion for $A_{k1}$ algebra

Discrete Painlevé equations from nonisospectral soliton equations

A study of the continuous and discrete Gambier systems

Discrete surfaces of revolution

KacMoodyVirasoro algebras and integrability of certain higher dimensional nonlinear evolutionary equations

Different faces of harmonic oscillator

Nonsymmetric linear difference equations for multiple orthogonal polynomials

Asymptotics for solution to the Cauchy problem for Volterra lattice with steplike initial values

Complexity and integrability

Strongly recommend this volume to all libraries of research institutions and to mathematicians with interest in difference equations.
CMS Notes