This work is dedicated to some notes on the Moyal momentum algebras applied to the sl_3 Boussinesq integrable hierarchy. Starting from a brief review of the Moyal momentum algebra structures, we establish in detail the Non-commutative Boussinesq hierarchy by using the Lax pair Generating Technique. Then we shows that these equations can be obtained as 3-reduction of Non-commutative KP hierarchy in a similarly form via some conformal realizations.
| Published in |
International Journal of Sustainable and Green Energy (Volume 4, Issue 3-2)
This article belongs to the Special Issue Wind-Generated Waves, 2D Integrable KdV Hierarchies and Solitons |
| DOI | 10.11648/j.ijrse.s.2015040302.14 |
| Page(s) | 17-22 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2014. Published by Science Publishing Group |
Moyal Momentum Algebra, Moyal KP Hierarchy, Non-Commutative Boussinesq Hierarchy
| [1] | A.B. Zamolodchikov, Integrable field theory from conformal field theory, Proceedings of the Taniguchi Symposium, Kyoto, (1988); Int. J. Mod. Phys. A3 (1988) 743; |
| [2] | A. Das and Z. Popowicz, Phys. Lett. A272 (2000) 65. [3] Szablikowski B.M. and Blaszak M., Meromorphic Lax representations of (1+1)-dimensional multi-Hamiltonian dispersionless systems, J. Math. Phys. 47 paper 092701 (2006); |
| [3] | M. Hamanaka and K. Toda, Phys. Lett. A 316 (2003) 77; |
| [4] | J. Madore An Introduction to Non-commutative Geometry and its Physical Applications Second Edition LMS 257 (1999); |
| [5] | Kontsevich M., Intersection theory of the moduli space of curves and the matrix Airy function, Comm. Math. Phys. 147 1-23 (1992); |
| [6] | M. T. Grisaru, L. Mazzanti, S. Penati, L. Tamassia, JHEP 0404:057, 2004; |
| [7] | M.B. Sedra, Moyal non-commutative integrability and the BurgersKdV mapping, Nuclear Physics B 740 [PM] (2006) 243270; |
| [8] | A. F. Dimakis and F. Muller-Hoissen, Rep. Math. Phys. 46 (2000) 203; Non-Commutative Kortewegde-Vries equation, hep-th 0007074; |
| [9] | A. Connes, Non-commutative geometry, Academic Press (1994); |
| [10] | B. A. Kupershmidt, Phys. Lett. A 102, 213 (1984); |
| [11] | M. H. Tlili AFST 6e srie, Tome 9, No 3 (2000), P. 551-564; |
| [12] | Strachan, I.A.B., The Moyal bracket and the dispersionless limit of the KP hierarchy, J. Phys. A. 20 (1995) 1967-1975; |
| [13] | A. Das and Z. Popowicz, J. Phys. A, Math.Gen. 34, 6105 (2001) and [hep- th/0104191]; B. A. Kupershmidt, Lett. Math. Phys. 20, 19 (1990); |
| [14] | A. Boulahoual and M. B. Sedra, hep-th/0208200, Chin. J. Phys 43, 408 (2005); A. Das and Z. Popowicz, Properties of Moyal-Lax Representation Phys. Lett. B 510 (2001) 264270 ; O. Dafounansou, A. El Boukili and M. B. Sedra,Some Aspects of Moyal Deformed Integrable Systems Chin. J. Phys 44, 274 (2006); |
| [15] | O. Babelon, D. Bernard, M. Talon, Introduction to Classical Integrable System Cambridge University Press (2003) and references therein; |
| [16] | A. F. Dimakis and F. Muller-Hoissen, J. Phys. A: Math. Theor. 40 (2007) 7573 - 7596; O. Lechtenfeld and A. D. Popov, Non-commutative Multi- solitons in (2+1)dimensions, JHEP 0111(2001)040; |
| [17] | Dai Zheng-De, Jiang Mu-Rung, Dai Qing-Yun, Li Shao-Lin; Chin.Phys.Lett. Vol.23, No 5 (2006)1065. |
APA Style
O. Dafounansou, D. C. Mbah, A. Boulahoual, M. B. Sedra. (2014). Notes on the Boussinesq Integrable Hierarchy. International Journal of Sustainable and Green Energy, 4(3-2), 17-22. https://doi.org/10.11648/j.ijrse.s.2015040302.14
ACS Style
O. Dafounansou; D. C. Mbah; A. Boulahoual; M. B. Sedra. Notes on the Boussinesq Integrable Hierarchy. Int. J. Sustain. Green Energy 2014, 4(3-2), 17-22. doi: 10.11648/j.ijrse.s.2015040302.14
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Download@article{10.11648/j.ijrse.s.2015040302.14,
author = {O. Dafounansou and D. C. Mbah and A. Boulahoual and M. B. Sedra},
title = {Notes on the Boussinesq Integrable Hierarchy},
journal = {International Journal of Sustainable and Green Energy},
volume = {4},
number = {3-2},
pages = {17-22},
doi = {10.11648/j.ijrse.s.2015040302.14},
url = {https://doi.org/10.11648/j.ijrse.s.2015040302.14},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijrse.s.2015040302.14},
abstract = {This work is dedicated to some notes on the Moyal momentum algebras applied to the sl_3 Boussinesq integrable hierarchy. Starting from a brief review of the Moyal momentum algebra structures, we establish in detail the Non-commutative Boussinesq hierarchy by using the Lax pair Generating Technique. Then we shows that these equations can be obtained as 3-reduction of Non-commutative KP hierarchy in a similarly form via some conformal realizations.},
year = {2014}
}
TY - JOUR T1 - Notes on the Boussinesq Integrable Hierarchy AU - O. Dafounansou AU - D. C. Mbah AU - A. Boulahoual AU - M. B. Sedra Y1 - 2014/12/15 PY - 2014 N1 - https://doi.org/10.11648/j.ijrse.s.2015040302.14 DO - 10.11648/j.ijrse.s.2015040302.14 T2 - International Journal of Sustainable and Green Energy JF - International Journal of Sustainable and Green Energy JO - International Journal of Sustainable and Green Energy SP - 17 EP - 22 PB - Science Publishing Group SN - 2575-1549 UR - https://doi.org/10.11648/j.ijrse.s.2015040302.14 AB - This work is dedicated to some notes on the Moyal momentum algebras applied to the sl_3 Boussinesq integrable hierarchy. Starting from a brief review of the Moyal momentum algebra structures, we establish in detail the Non-commutative Boussinesq hierarchy by using the Lax pair Generating Technique. Then we shows that these equations can be obtained as 3-reduction of Non-commutative KP hierarchy in a similarly form via some conformal realizations. VL - 4 IS - 3-2 ER -
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