Symmetries and Integrability of Difference Equations
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Part of London Mathematical Society Lecture Note Series
 Editors:
 Peter A. Clarkson, University of Kent, Canterbury
 Frank W. Nijhoff, University of Leeds
 Date Published: May 2012
 availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
 format: Adobe eBook Reader
 isbn: 9781139244107
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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.
Read more Exciting area of research
 Articles by top names
 Links with mathematical physics
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'… 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
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×Product details
 Date Published: May 2012
 format: Adobe eBook Reader
 isbn: 9781139244107
 availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
Table of Contents
Part I. Partial Differential Equations:
1. Discrete linearisable Gambier equations A. K. Common, E. Hesameddini and M. Musette
2. Generalized Bäcklund transformation and new explicit solutions of the twodimensional Toda equation X.B. Hu and P. Clarkson
3. Different aspects of relativistic Toda Chain S. Kharchev, A. Mironov, A. Zhedanov
Part II. Integrable Mappings:
4. Integrable symplectic maps A. Fordy
5. An iterative process on quartics and integrable symplectic maps J. P. Francoise, and O. Ragnisco
6. Integrable mappings of KdV type and hyperelliptic addition theorems F. Nijhoff and V. Z. Enolskii
7. Rmatrix hierarchies, integrable lattice systems and their integrable discretizations Y. Suris
Part III. Discrete Geometry:
8. Discrete conformal maps and surfaces A. Bobenko
9. The Bäcklund transformation for discrete isothermic surfaces J. Cieslinski
10. Integrable discrete geometry with ruler and compass A. Doliwa
11. Selfdual Einstein spaces and a discrete Tzitzeica equation. A permutability theorem link W. K. Schief
Part IV. Asymptotic Analysis:
12. New solutions of the nonstationary Schrödinger and KadomtsevPetviashvili equation M. Ablowitz
13. On asymptotic analysis of the orthogonal polynomials via the RiemannHilbert method P. Bleher and A. Its
14. A new spectral transform for solving the continuous and spatially discrete heat equation on simple trees P. C. Bressloff and A. Fokas
Part V. Discrete Painlevé Equations:
15. The discrete Painlevé hierarchy C. Cresswell and N. Joshi
16. Rational solutions to dPIV J. Hietarinta and K. Kajiwara
17. The discrete Painlevé II equation and the classical special functions K. Kajiwara
18. Freud's equations for orthogonal polynomials as discrete Painlevé equations A. Magnus
Part VI. Symmetries of Difference Equations:
19. An approach to master symmetries of lattice equations B. Fuchssteiner and W. X. Ma
20. Symmetries and generalized symmetries for discrete dynamical systems D. Levi
21. Nonlinear difference equations with superposition formulas P. Winternitz
Part VII. Numerical Methods and Miscellaneous:
22. Generalising the Painlevé truncation: expansions in Riccati pseudopotentials A. Fordy and A. Pickering
23. Symplectic RungeKutta schemes W. Oevel
Part VIII. Cellular Automata:
24. Soliton cellular automata C. Gilson
25. Painlevé equations and cellular automata B. Grammaticos and A. Ramani
26. 2+1 Dimensional soliton cellular automaton S. Moriwaki, A. Nagaki, J. Satsuma, T. Tokihiro, M. Torii, D. Takahashi and J. Matsukidaira
Part IX. qSpecial Functions and qDifference Equations:
27. Fourier–Gauss transforms of qexponential and qBessel functions N. Atakishiyev
28. The Wilson bispectral involution: some elementary examples F. A. Grünbaum and L. Haine
29. Factorisation of Macdonald polynomials V. B. Kuztensov and E. K. Skylanin
30. Local YangBaxter relations associated with Hirota's discrete equation R. Kashaev
31. Ultradiscrete soliton systems J. Satsuma
32. Schrödinger equation on quantum homogeneous spaces F. Bonechi, R. Giachetti, E. Sorace, M. Tarlini
33. Some algebraic solutions of discrete equations from anticommuting variables C. Viallet
34. Qcombinatorics and quantum integrability A. Volkov.
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