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Sommario
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 two-dimensional 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. R-matrix 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. Self-dual Einstein spaces and a discrete Tzitzeica equation. A permutability theorem link W. K. Schief; Part IV. Asymptotic Analysis: 12. New solutions of the non-stationary Schrödinger and Kadomtsev-Petviashvili equation M. Ablowitz; 13. On asymptotic analysis of the orthogonal polynomials via the Riemann-Hilbert 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 d-PIV 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 Runge-Kutta 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. q-Special Functions and q-Difference Equations: 27. Fourier-Gauss transforms of q-exponential and q-Bessel 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 Yang-Baxter relations associated with Hirota's discrete equation R. Kashaev; 31. Ultra-discrete 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. Q-combinatorics and quantum integrability A. Volkov.
Riassunto
In recent years there has been a remarkable growth of interest in discrete integrable systems. Connections have been made with 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.
