On some integrable discrete-time systems associated with the Bogoyavlensky lattices

Physica A: Statistical Mechanics and its Applications

Volumn 228, Issue 1-4, 1996, Pages 172-188

  Papageorgiou, Vassilios G ^a   Nijhoff, Frank W ^b  

^a TECHNICAL UNIVERSITY OF CRETE   (Greece)

^b UNIVERSITY OF LEEDS   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFERENCE EQUATIONS; DIFFERENTIAL EQUATIONS; INTEGRATION; MATHEMATICAL TECHNIQUES; NUMERICAL METHODS;

BOGOYAVLENSKY LATTICES; FINITE DIMENSIONAL REDUCTIONS; INTEGRABLE DISCRETE TIME SYSTEMS; PAINLEVE EQUATION; TIME DISCRETISATIONS;

INTEGRAL EQUATIONS;

EID: 0030164180     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/0378-4371(95)00440-8     Document Type: Article

References (42)

1. O.I. Bogoyavlensky, Phys. Lett. A 134 (1988) 34.
2. O.I. Bogoyavlensky, Math. USSR Izv. 31 (1988) 435; 32 (1989) 39.
3. O.I. Bogoyavlensky, Math. USSR Izv. 31 (1988) 435; 32 (1989) 39.
4. K. Narita, J. Phys. Soc. Japan 51 (1982) 1682.
5. A. Belov and K.D. Chaltikian, Phys. Lett. B 309 (1993) 268; 317 (1993) 64,73.
6. A. Belov and K.D. Chaltikian, Phys. Lett. B 309 (1993) 268; 317 (1993) 64,73.
7. J.L. Gervais, Phys. Lett. B 160 (1985) 277,279.
8. L.D. Faddeev and L.A. Takhtadzhyan, Springer Lect. Notes Phys. 246 (1986) 166.
9. A.Yu. Volkov, Theor. Math. Phys. 74 (1988) 96.
10. A.Yu. Volkov, Phys. Lett. A 167 (1992) 345.
11. F.W. Nijhoff, V.G. Papageorgiou, H.W. Capel and G.R.W. Quispel, Inv. Probl. 8 (1992) 597.
12. F.W. Nijhoff and H.W. Capel, Acta Applicandae Mathematicae 39 (1995) 133.
13. B. Grammaticos and A. Ramani, Discrete Painlevé Equations: Derivation and Properties, in:Applications of Geometric and Analytic Methods to Nonlinear Differential equations, P.A. Clarkson, ed., NATO-ASI Series C, Vol. 413 (Kluwer Academic Publishers, Dordrecht, 1993) p. 299.
14. F.W. Nijhoff, V.G. Papageorgiou and H.W. Capel, Integrable Time-Discrete Systems: Lattices and Mappings, in: Quantum Groups, P.P. Kulish, ed., Springer LNM 1510 (1992) p. 312.
15. V.G Papageorgiou, B. Grammaticos and A. Ramani, Physics Lett. A 179 (1993) 111.
16. V.G Papageorgiou, B. Grammaticos and A. Ramani, Orthogonal Polynomial Approach to Discrete Lax Pairs for Initial-Value-Boundary Problems of the QD-Algorithm, Letters Math. Phys. 34 (1995) 91.
17. L.D. Faddeev and A.Yu. Volkov, Phys. Lett. B 315 (1993) 311.
18. A.Yu. Volkov and L.D. Faddeev, Theor. Math. Phys. 92 (1993) 837.
19. F.W. Nijhoff, Lett. Math. Phys. 30 (1994) 327.
20. G. Wilson, On the Adler-Gel'fand-Dikii Bracket, Proc. of the CRM Worlshop om Hamiltonian Systems, Transformation Groups and Spectral Transform Methods, J. Harnad and J.E. Marsden, eds., CRM Lecture Notes Series (1990) p. 77.
21. J. Weiss, J. Math. Phys. 24 (1983) 1405.
22. F.W. Nijhoff, On some "Schwarzian" Equations and their Discrete Analogues, in: Memorial Volume for I.Ya. Dorfman, A.S. Fokas and I.M. Gel'fand, eds. (Birkhäuser, Basel), to be published.
23. V.G. Papageorgiou, F.W. Nijhoff and H.W. Capel, Phys. Lett. A 147 (1990) 106.
24. H.W. Capel, F.W. Nijhoff and V.G. Papageorgiou, Phys. Lett. A 155 (1991) 377.
25. Y. Nakamura and T. Hashimoto, Phys. Lett. A 193 (1994) 42.
26. R. Hirota, S. Tsujimoto and T. Imai, in: Future Directions of Nonlinear Dynamics in Physical and Biological Systems, P.L. Christiansen et al., eds (Plenum Press, New York, 1993) pp. 7-14.
27. A.P. Veselov, Integrable Maps, Russ. Math. Surv. 46 (1991) 1.
28. M. Bruschi, O. Ragnisco, P.M. Santini and G.-Z. Tu, Physica D 49 (1991) 273.
29. V.G. Papageorgiou, F.W. Nijhoff, B. Grammaticos and A. Ramani, Phys. Lett. A 164 (1992) 57.
30. H. Zhang, G.-Z. Tu, W. Oevel and B. Fuchssteiner, J. Math. Phys. 32 (1991) 1908.
31. Yu.B. Suris, Phys. Lett. A 188 (1994) 256.
32. E. Brézin and V.A. Kazakov, Phys. Lett. B 236 (1990) 144.
33. D. J. Gross and A.A. Migdal, Phys. Rev. Lett. 64 (1990) 127; Nucl. Phys. B 340 (1990) 333.
34. D. J. Gross and A.A. Migdal, Phys. Rev. Lett. 64 (1990) 127; Nucl. Phys. B 340 (1990) 333.
35. A.S. Fokas, A.R. Its and A. Kitaev, Commun. Math. Phys. 142 (1991) 313.
36. C. Brezinski, Biorthogonality and its Applications to Numerical Analysis, Monographs in Pure and Applied Mathematics, Vol. 155 (Marcel Dekker, New York, 1992).
37. C. Brezinski, A Unified Approach to Various Orthogonalities, Ann. de la Fac. de Toulouse, Vol. 1, Nr. 3 (1992).
38. K. Douak and P. Maroni, Les Polynômes Orthogonaux "Classiques" de Dimension Deux, Analysis 12 (1992) 71.
39. Al.B. Zamolodchikov, Phys. Lett. B 253 (1991) 391; Nucl. Phys. B 358 (1991) 497.
40. Al.B. Zamolodchikov, Phys. Lett. B 253 (1991) 391; Nucl. Phys. B 358 (1991) 497.
41. P. Fendley and H. Saleur, Nucl. Phys. B 388 (1992) 609.
42. F. Gliozzi and R. Tateo, ADE functional dilogarithm identities and integrable models, Preprint DFTT-39/94.