著者紹介

内容

目次

Part I. Partial Differential Equations: 1. Discrete linearisable Gambierequations A. K. Common, E. Hesameddini and M. Musette; 2. GeneralizedBacklund transformation and new explicit solutions of the two-dimensionalToda equation X.-B. Hu and P. Clarkson; 3. Different aspects of relativisticToda Chain S. Kharchev, A. Mironov, A. Zhedanov; Part II. IntegrableMappings: 4. Integrable symplectic maps A. Fordy; 5. An iterative process onquartics 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 latticesystems and their integrable discretizations Y. Suris; Part III. DiscreteGeometry: 8. Discrete conformal maps and surfaces A. Bobenko; 9. The Backlundtransformation for discrete isothermic surfaces J. Cieslinski; 10. Integrablediscrete geometry with ruler and compass A. Doliwa; 11. Self-dual Einsteinspaces and a discrete Tzitzeica equation. A permutability theorem link W. K.Schief; Part IV. Asymptotic Analysis: 12. New solutions of the non-stationarySchrodinger and Kadomtsev-Petviashvili equation M. Ablowitz; 13. Onasymptotic analysis of the orthogonal polynomials via the Riemann-Hilbertmethod P. Bleher and A. Its; 14. A new spectral transform for solving thecontinuous and spatially discrete heat equation on simple trees P. C.Bressloff and A. Fokas; Part V. Discrete Painleve Equations: 15. The discretePainleve hierarchy C. Cresswell and N. Joshi; 16. Rational solutions to d-PIVJ. Hietarinta and K. Kajiwara; 17. The discrete Painleve II equation and theclassical special functions K. Kajiwara; 18. Freud's equations for orthogonalpolynomials as discrete Painleve equations A. Magnus; Part VI. Symmetries ofDifference Equations: 19. An approach to master symmetries of latticeequations B. Fuchssteiner and W. X. Ma; 20. Symmetries and generalizedsymmetries for discrete dynamical systems D. Levi; 21. Nonlinear differenceequations with superposition formulas P. Winternitz; Part VII. NumericalMethods and Miscellaneous: 22. Generalising the Painleve 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. Painleve equations and cellularautomata B. Grammaticos and A. Ramani; 26. 2+1 Dimensional soliton cellularautomaton S. Moriwaki, A. Nagaki, J. Satsuma, T. Tokihiro, M. Torii, D.Takahashi and J. Matsukidaira; Part IX. q-Special Functions and q-DifferenceEquations: 27. Fourier-Gauss transforms of q-exponential and q-Besselfunctions N. Atakishiyev; 28. The Wilson bispectral involution: someelementary examples F. A. Grunbaum and L. Haine; 29. Factorisation ofMacdonald polynomials V. B. Kuztensov and E. K. Skylanin; 30. LocalYang-Baxter relations associated with Hirota's discrete equation R. Kashaev;31. Ultra-discrete soliton systems J. Satsuma; 32. Schrodinger equation onquantum homogeneous spaces F. Bonechi, R. Giachetti, E. Sorace, M. Tarlini;33. Some algebraic solutions of discrete equations from anticommutingvariables C. Viallet; 34. Q-combinatorics and quantum integrability A. Volkov.