Bi-differential calculi and integrable models

Journal of Physics A: Mathematical and General

Volumn 33, Issue 5, 2000, Pages 957-974

  Dimakis, A ^a   Muller Hoissen F ^b  

^a UNIVERSITY OF THE AEGEAN   (Greece)

^b MAX PLANCK INSTITUTE FOR DYNAMICS AND SELF ORGANIZATION   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040435681     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/33/5/311     Document Type: Article

References (40)

1. Lüscher M and Pohlmeyer K 1978 Scattering of massless lumps and non-local charges in the two-dimensional classical non-linear σ-model Nucl. Phys. B 137 46-54
2. Brezin E, Itzykson C, Zinn-Justin J and Zuber J-B 1979 Remarks about the existence of non-local charges in two-dimensional models Phys. Lett. B 82 442-4
3. Dimakis A and Müller-Hoissen F 1996 Integrable discretizations of chiral models via deformation of the differential calculus J. Phys. A: Math. Gen. 29 5007-18
4. Dimakis A and Müller-Hoissen F 1997 Noncommutative geometry and integrable models Lett. Math. Phys. 39 69-79
5. Dimakis A and Müller-Hoissen F 1998 Noncommutative geometry and a class of completely integrable models Czech. J. Phys. 48 1319-24
6. Hénon M 1974 Integrals of the Toda lattice Phys. Rev. B 9 1921-3
7. Plebański J 1975 Some solutions of complex Einstein equations J. Math. Phys. 16 2395-402
8. Takasaki K 1989 An infinite number of hidden variables in hyper-Kähler metrics J. Math. Phys. 30 1515-21
9. Fuchs D B, Gabrielov A M and Gel'fand I M 1976 The Gauss-Bonnet theorem and the Atiyah-Patodi-Singer functionals for the characteristic classes of foliations Topology 15 165-88
10. Vinogradov A M 1978 A spectral sequence associated with a nonlinear differential equation, and algebro-geometric foundations of Lagrangian field theory with constraints Sov. Math.-Dokl. 19 144-8
11. Tulczyjew W M 1980 The Euler-Lagrange resolution Differential Geometric Methods in Mathematical Physics (Lecture Notes in Mathematics vol 836) ed P L Garcia, A Pérez-Rendón and J M Souriau (Berlin: Springer) pp 22-48
12. Torre C G 1997 Local cohomology in field theory with applications to the Einstein equations Preprint hep-th/9706092
13. Husain V 1994 Self-dual gravity as a two-dimensional theory and conservation laws Class. Quantum Grav. 11 927-37
14. Husain V 1995 The affine symmetry of self-dual gravity J. Math. Phys. 36 6897-906
15. Strachan I A B 1995 The symmetry structure of the anti-self-dual Einstein hierarchy J. Math. Phys. 36 3566-73
16. Grant J D E and Strachan I A B 1998 Hypercomplex integrable systems Preprint solv-int/9808019
17. Curtright T and Zachos C 1994 Currents, charges, and canonical structure of pseudodual chiral models Phys. Rev. D 49 5408-21
18. Zakharov V E and Mikhailov A V 1978 Relativistically invariant two-dimensional models of field theory which are integrable by means of the inverse scattering problem method Sov. Phys.-JETP 47 1017-27
19. Nappi C R 1980 Some properties of an analogue of the chiral model Phys. Rev. D 21 418-20
20. Toda M 1981 Theory of Nonlinear Lattices (Berlin: Springer)
21. Dimakis A, Müller-Hoissen F and Striker T 1993 Non-commutative differential calculus and lattice gauge theory J. Phys. A: Math. Gen. 26 1927-49
22. Dimakis A and Müller-Hoissen F 1992 Quantum mechanics on a lattice and q-deformations Phys. Lett. B 295 242-8
23. Hirota R, Ito M and Kako F 1988 Two-dimensional Toda lattice equations Progr. Theor. Phys. Suppl. 94 42-58
24. Gekhman M 1998 Hamiltonian structure of non-Abelian Toda lattice Lett. Math. Phys. 46 189-205
25. Matsukidaira J, Satsuma J and Strampp W 1990 Conserved quantities and symmetries of KP hierarchy J. Math. Phys. 31 1426-34
26. Drazin P G and Johnson R S 1989 Solitons: An Introduction (Cambridge: Cambridge University Press)
27. Pohlmeyer K 1976 Integrable Hamiltonian systems and interactions through quadratic constraints Commun. Math. Phys. 46 207-21
28. Scott A C, Chu F Y F and McLaughlin D W 1973 The soliton: a new concept in applied science Proc. IEEE 61 1443-83
29. Ward R S 1984 Completely solvable gauge-field equations in dimension greater than four Nucl. Phys. 236 381-96
30. Yang C N 1977 Condition of self-duality for SU (2) gauge fields on Euclidean four-dimensional space Phys. Rev. Lett. 38 1377-9
31. Chau L-L 1983 Chiral fields, self-dual Yang-Mills fields as integrable systems, and the role of the Kac-Moody algebra (Lecture Notes in Physics vol 189) ed K B Wolf (Berlin: Springer) pp 110-27
32. Prasad M K, Sinha A and Chau Wang L-L 1979 Non-local continuity equations for self-dual SU(N) Yang-Mills fields Phys. Lett. B 87 237-8
33. Pohlmeyer K 1980 On the Lagrangian theory of anti-self-dual fields in four-dimensional Euclidean space Commun. Math. Phys. 72 37-47
34. Ablowitz M J, Kaup D J, Newell A C and Segur H 1974 The inverse scattering transform - Fourier analysis for nonlinear problems Stud. Appl. Math. 53 249-315
35. Faddeev L D and Takhtajan L A 1987 Hamiltonian Methods in the Theory of Solitons (Berlin: Springer)
36. Olver O J 1986 Applications of Lie Groups to Differential Equations (Berlin: Springer)
37. Hirota R 1976 Direct method of finding exact solutions of nonlinear evolution equations Bäcklund Transformations, the Inverse Scattering Method, Solitons, and their Applications ed R M Miura (Berlin: Springer) pp 40-68
38. Hirota R 1986 Reduction of soliton equations in bilinear form Physica D 18 161-70
39. Sato M 1981 Soliton equations as dynamical systems on infinite dimensional Grassmann manifolds RIMS-Kokyuroku 439 30-46
40. Jimbo M and Miwa T 1983 Solitons and infinite dimensional Lie algebras Publ. RIMS 19 943-1001