Symmetries and integrability of difference equations

著者

• Clarkson, P. A
• Nijhoff, Frank W
• London Mathematical Society
• International Conference on "Symmetries and Integrability of Difference Equations"

書誌事項

Symmetries and integrability of difference equations

edited by Peter A. Clarkson, Frank W. Nijhoff

（London Mathematical Society lecture note series, 255）

Cambridge University Press, 1999

注記

Includes bibliographical references

"The second international conference on "Symmetries and Integrability of Difference Equations" (SIDE II) was held at the University of Kent at Canterbury, July 1-5, 1996. It was the successor of a first meeting on the same topic held in Estérel (Québec, Canada)" -- Pref

内容説明・目次

内容説明

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.

目次

• Part I. Partial Differential Equations: 1. Discrete linearisable Gambier equations A. K. Common, E. Hesameddini and M. Musette
• 2. Generalized Backlund 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 Backlund 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 Schroedinger 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 Painleve Equations: 15. The discrete Painleve hierarchy C. Cresswell and N. Joshi
• 16. Rational solutions to d-PIV J. Hietarinta and K. Kajiwara
• 17. The discrete Painleve II equation and the classical special functions K. Kajiwara
• 18. Freud's equations for orthogonal polynomials as discrete Painleve 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 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 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. Grunbaum 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. Schroedinger 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.

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詳細情報

• NII書誌ID(NCID): BA39651496
• ISBN:
  • 0521596998
• 出版国コード: uk
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Cambridge
• ページ数/冊数: xvi, 424 p.
• 大きさ: 23 cm
• 分類:
  • DC21 : 515.625
  • NDC8 : 413.8
• 件名:
  • LCSH : Difference equations
  • LCSH : Symmetry groups
• 親書誌ID:
  • BA0005393X