Bicomplexes and integrable models

Journal of Physics A: Mathematical and General

Volumn 33, Issue 37, 2000, Pages 6579-6591

  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: 0040435634     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/33/37/310     Document Type: Article

References (42)

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2. Dimakis A and Müller-Hoissen F 1996 Soliton equations and the zero curvature condition in noncommutative geometry J. Phys. A: Math. Gen. 29 7279-86 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 Dimakis A and Müller-Hoissen F 1997 Noncommutative geometry and integrable models Lett. Math. Phys. 39 69-79 Dimakis A and Müller-Hoissen F 1998 Noncommutative geometry and a class of completely integrable models Czech. J. Phys. 48 1319-24
3. Dimakis A and Müller-Hoissen F 1996 Soliton equations and the zero curvature condition in noncommutative geometry J. Phys. A: Math. Gen. 29 7279-86 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 Dimakis A and Müller-Hoissen F 1997 Noncommutative geometry and integrable models Lett. Math. Phys. 39 69-79 Dimakis A and Müller-Hoissen F 1998 Noncommutative geometry and a class of completely integrable models Czech. J. Phys. 48 1319-24
4. Dimakis A and Müller-Hoissen F 1996 Soliton equations and the zero curvature condition in noncommutative geometry J. Phys. A: Math. Gen. 29 7279-86 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 Dimakis A and Müller-Hoissen F 1997 Noncommutative geometry and integrable models Lett. Math. Phys. 39 69-79 Dimakis A and Müller-Hoissen F 1998 Noncommutative geometry and a class of completely integrable models Czech. J. Phys. 48 1319-24
5. Dimakis A and Müller-Hoissen F 1996 Soliton equations and the zero curvature condition in noncommutative geometry J. Phys. A: Math. Gen. 29 7279-86 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 Dimakis A and Müller-Hoissen F 1997 Noncommutative geometry and integrable models Lett. Math. Phys. 39 69-79 Dimakis A and Müller-Hoissen F 1998 Noncommutative geometry and a class of completely integrable models Czech. J. Phys. 48 1319-24
6. Dimakis A and Müller-Hoissen F 2000 Bi-differential calculi and integrable models J. Phys. A: Math. Gen. 33 957-74
7. Dimakis A and Müller-Hoissen F 1999 Bi-differential calculus and the KdV equation Rep. Math. Phys. at press ( Dimakis A and Müller-Hoissen F 1999 Preprint math-ph/9908016)
8. Dimakis A and Müller-Hoissen F 1999 Bi-differential calculus and the KdV equation Rep. Math. Phys. at press (Dimakis A and Müller-Hoissen F 1999 Preprint math-ph/9908016)
9. Dimakis A and Müller-Hoissen F 1999 Bicomplexes and finite Toda lattices Quantum Theory and Symmetries ed H-D Doebner, V K Dobrev, J-D Hennig and W Lücke (Singapore: World Scientific) pp 545-9 (Dimakis A and Müller-Hoissen F 1999 Preprint solv-int/9911006)
10. Dimakis A and Müller-Hoissen F 1999 Bicomplexes and finite Toda lattices Quantum Theory and Symmetries ed H-D Doebner, V K Dobrev, J-D Hennig and W Lücke (Singapore: World Scientific) pp 545-9 (Dimakis A and Müller-Hoissen F 1999 Preprint solv-int/9911006)
11. Witten E 1977 Some exact multipseudoparticle solutions of classical Yang-Mills theory Phys. Rev. Lett. 38 121-4 Ward R S 1985 Integrable and solvable systems and relations among them Phil. Trans. R. Soc. A 315 451-7 Mason L J and Sparling G A J 1989 Nonlinear Schrödinger and Korteweg-De Vries are reductions of selfdual Yang-Mills Phys. Lett. A 137 29-33 Mason L J and Sparling G A J 1992 Twistor correspondences for the soliton hierarchies J. Geom. Phys. 8 243-71 Ivanova T A and Popov A D 1992 Soliton equations and self-dual gauge fields Phys. Lett. A 170 293-9 Ivanova T A and Popov A D 1995 Some new integrable equations from the self-dual Yang-Mills equations Phys. Lett. A 205 158-66 Castro C 1993 The KP equation from Plebanski and SU(∞) self-dual Yang-Mills Preprint hep-th/9308101 Guil F and Mañas M 1994 Two-dimensional integrable systems and self-dual Yang-Mills equations J. Math. Phys. 35 2902-13 Legare M 1996 Symmetry reductions of the Lax pair of the four-dimensional Euclidean self-dual Yang-Mills equations J. Nonlinear. Math. Phys. 3 266-85 Fehér L and Gábor A 2000 A note on the appearance of self-dual Yang-Mills fields in integrable hierarchies Preprint nlin.SI/0002003 ( J. Nonlinear Math. Phys. at press)
12. Witten E 1977 Some exact multipseudoparticle solutions of classical Yang-Mills theory Phys. Rev. Lett. 38 121-4 Ward R S 1985 Integrable and solvable systems and relations among them Phil. Trans. R. Soc. A 315 451-7 Mason L J and Sparling G A J 1989 Nonlinear Schrödinger and Korteweg-De Vries are reductions of selfdual Yang-Mills Phys. Lett. A 137 29-33 Mason L J and Sparling G A J 1992 Twistor correspondences for the soliton hierarchies J. Geom. Phys. 8 243-71 Ivanova T A and Popov A D 1992 Soliton equations and self-dual gauge fields Phys. Lett. A 170 293-9 Ivanova T A and Popov A D 1995 Some new integrable equations from the self-dual Yang-Mills equations Phys. Lett. A 205 158-66 Castro C 1993 The KP equation from Plebanski and SU(∞) self-dual Yang-Mills Preprint hep-th/9308101 Guil F and Mañas M 1994 Two-dimensional integrable systems and self-dual Yang-Mills equations J. Math. Phys. 35 2902-13 Legare M 1996 Symmetry reductions of the Lax pair of the four-dimensional Euclidean self-dual Yang-Mills equations J. Nonlinear. Math. Phys. 3 266-85 Fehér L and Gábor A 2000 A note on the appearance of self-dual Yang-Mills fields in integrable hierarchies Preprint nlin.SI/0002003 ( J. Nonlinear Math. Phys. at press)
13. Witten E 1977 Some exact multipseudoparticle solutions of classical Yang-Mills theory Phys. Rev. Lett. 38 121-4 Ward R S 1985 Integrable and solvable systems and relations among them Phil. Trans. R. Soc. A 315 451-7 Mason L J and Sparling G A J 1989 Nonlinear Schrödinger and Korteweg-De Vries are reductions of selfdual Yang-Mills Phys. Lett. A 137 29-33 Mason L J and Sparling G A J 1992 Twistor correspondences for the soliton hierarchies J. Geom. Phys. 8 243-71 Ivanova T A and Popov A D 1992 Soliton equations and self-dual gauge fields Phys. Lett. A 170 293-9 Ivanova T A and Popov A D 1995 Some new integrable equations from the self-dual Yang-Mills equations Phys. Lett. A 205 158-66 Castro C 1993 The KP equation from Plebanski and SU(∞) self-dual Yang-Mills Preprint hep-th/9308101 Guil F and Mañas M 1994 Two-dimensional integrable systems and self-dual Yang-Mills equations J. Math. Phys. 35 2902-13 Legare M 1996 Symmetry reductions of the Lax pair of the four-dimensional Euclidean self-dual Yang-Mills equations J. Nonlinear. Math. Phys. 3 266-85 Fehér L and Gábor A 2000 A note on the appearance of self-dual Yang-Mills fields in integrable hierarchies Preprint nlin.SI/0002003 ( J. Nonlinear Math. Phys. at press)
14. Witten E 1977 Some exact multipseudoparticle solutions of classical Yang-Mills theory Phys. Rev. Lett. 38 121-4 Ward R S 1985 Integrable and solvable systems and relations among them Phil. Trans. R. Soc. A 315 451-7 Mason L J and Sparling G A J 1989 Nonlinear Schrödinger and Korteweg-De Vries are reductions of selfdual Yang-Mills Phys. Lett. A 137 29-33 Mason L J and Sparling G A J 1992 Twistor correspondences for the soliton hierarchies J. Geom. Phys. 8 243-71 Ivanova T A and Popov A D 1992 Soliton equations and self-dual gauge fields Phys. Lett. A 170 293-9 Ivanova T A and Popov A D 1995 Some new integrable equations from the self-dual Yang-Mills equations Phys. Lett. A 205 158-66 Castro C 1993 The KP equation from Plebanski and SU(∞) self-dual Yang-Mills Preprint hep-th/9308101 Guil F and Mañas M 1994 Two-dimensional integrable systems and self-dual Yang-Mills equations J. Math. Phys. 35 2902-13 Legare M 1996 Symmetry reductions of the Lax pair of the four-dimensional Euclidean self-dual Yang-Mills equations J. Nonlinear. Math. Phys. 3 266-85 Fehér L and Gábor A 2000 A note on the appearance of self-dual Yang-Mills fields in integrable hierarchies Preprint nlin.SI/0002003 ( J. Nonlinear Math. Phys. at press)
15. Witten E 1977 Some exact multipseudoparticle solutions of classical Yang-Mills theory Phys. Rev. Lett. 38 121-4 Ward R S 1985 Integrable and solvable systems and relations among them Phil. Trans. R. Soc. A 315 451-7 Mason L J and Sparling G A J 1989 Nonlinear Schrödinger and Korteweg-De Vries are reductions of selfdual Yang-Mills Phys. Lett. A 137 29-33 Mason L J and Sparling G A J 1992 Twistor correspondences for the soliton hierarchies J. Geom. Phys. 8 243-71 Ivanova T A and Popov A D 1992 Soliton equations and self-dual gauge fields Phys. Lett. A 170 293-9 Ivanova T A and Popov A D 1995 Some new integrable equations from the self-dual Yang-Mills equations Phys. Lett. A 205 158-66 Castro C 1993 The KP equation from Plebanski and SU(∞) self-dual Yang-Mills Preprint hep-th/9308101 Guil F and Mañas M 1994 Two-dimensional integrable systems and self-dual Yang-Mills equations J. Math. Phys. 35 2902-13 Legare M 1996 Symmetry reductions of the Lax pair of the four-dimensional Euclidean self-dual Yang-Mills equations J. Nonlinear. Math. Phys. 3 266-85 Fehér L and Gábor A 2000 A note on the appearance of self-dual Yang-Mills fields in integrable hierarchies Preprint nlin.SI/0002003 ( J. Nonlinear Math. Phys. at press)
16. Witten E 1977 Some exact multipseudoparticle solutions of classical Yang-Mills theory Phys. Rev. Lett. 38 121-4 Ward R S 1985 Integrable and solvable systems and relations among them Phil. Trans. R. Soc. A 315 451-7 Mason L J and Sparling G A J 1989 Nonlinear Schrödinger and Korteweg-De Vries are reductions of selfdual Yang-Mills Phys. Lett. A 137 29-33 Mason L J and Sparling G A J 1992 Twistor correspondences for the soliton hierarchies J. Geom. Phys. 8 243-71 Ivanova T A and Popov A D 1992 Soliton equations and self-dual gauge fields Phys. Lett. A 170 293-9 Ivanova T A and Popov A D 1995 Some new integrable equations from the self-dual Yang-Mills equations Phys. Lett. A 205 158-66 Castro C 1993 The KP equation from Plebanski and SU(∞) self-dual Yang-Mills Preprint hep-th/9308101 Guil F and Mañas M 1994 Two-dimensional integrable systems and self-dual Yang-Mills equations J. Math. Phys. 35 2902-13 Legare M 1996 Symmetry reductions of the Lax pair of the four-dimensional Euclidean self-dual Yang-Mills equations J. Nonlinear. Math. Phys. 3 266-85 Fehér L and Gábor A 2000 A note on the appearance of self-dual Yang-Mills fields in integrable hierarchies Preprint nlin.SI/0002003 ( J. Nonlinear Math. Phys. at press)
17. Witten E 1977 Some exact multipseudoparticle solutions of classical Yang-Mills theory Phys. Rev. Lett. 38 121-4 Ward R S 1985 Integrable and solvable systems and relations among them Phil. Trans. R. Soc. A 315 451-7 Mason L J and Sparling G A J 1989 Nonlinear Schrödinger and Korteweg-De Vries are reductions of selfdual Yang-Mills Phys. Lett. A 137 29-33 Mason L J and Sparling G A J 1992 Twistor correspondences for the soliton hierarchies J. Geom. Phys. 8 243-71 Ivanova T A and Popov A D 1992 Soliton equations and self-dual gauge fields Phys. Lett. A 170 293-9 Ivanova T A and Popov A D 1995 Some new integrable equations from the self-dual Yang-Mills equations Phys. Lett. A 205 158-66 Castro C 1993 The KP equation from Plebanski and SU(∞) self-dual Yang-Mills Preprint hep-th/9308101 Guil F and Mañas M 1994 Two-dimensional integrable systems and self-dual Yang-Mills equations J. Math. Phys. 35 2902-13 Legare M 1996 Symmetry reductions of the Lax pair of the four-dimensional Euclidean self-dual Yang-Mills equations J. Nonlinear. Math. Phys. 3 266-85 Fehér L and Gábor A 2000 A note on the appearance of self-dual Yang-Mills fields in integrable hierarchies Preprint nlin.SI/0002003 ( J. Nonlinear Math. Phys. at press)
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