Notes on the Boussinesq Integrable Hierarchy
International Journal of Sustainable and Green Energy
Volume 4, Issue 3-2, May 2015, Pages: 17-22
Received: Nov. 20, 2014; Accepted: Nov. 28, 2014; Published: Dec. 15, 2014
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O. Dafounansou, Department of Physics, Faculty of Science, Douala University, Douala, Cameroun
D. C. Mbah, CEPAMOQ, Douala University, Douala, Cameroun
A. Boulahoual, LHESIR, Faculty of Science of Kenitra, Ibn Toufail University, Kenitra, Morocco
M. B. Sedra, LHESIR, Faculty of Science of Kenitra, Ibn Toufail University, Kenitra, Morocco; ENSAH, Mohammed First University, Al Hoceima, Morocco
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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.
Moyal Momentum Algebra, Moyal KP Hierarchy, Non-Commutative Boussinesq Hierarchy
To cite this article
O. Dafounansou, D. C. Mbah, A. Boulahoual, M. B. Sedra, Notes on the Boussinesq Integrable Hierarchy, International Journal of Sustainable and Green Energy. Special Issue: Wind-Generated Waves, 2D Integrable KdV Hierarchies and Solitons. Vol. 4, No. 3-2, 2015, pp. 17-22. doi: 10.11648/j.ijrse.s.2015040302.14
A.B. Zamolodchikov, Integrable field theory from conformal field theory, Proceedings of the Taniguchi Symposium, Kyoto, (1988); Int. J. Mod. Phys. A3 (1988) 743;
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);
M. Hamanaka and K. Toda, Phys. Lett. A 316 (2003) 77;
J. Madore An Introduction to Non-commutative Geometry and its Physical Applications Second Edition LMS 257 (1999);
Kontsevich M., Intersection theory of the moduli space of curves and the matrix Airy function, Comm. Math. Phys. 147 1-23 (1992);
M. T. Grisaru, L. Mazzanti, S. Penati, L. Tamassia, JHEP 0404:057, 2004;
M.B. Sedra, Moyal non-commutative integrability and the BurgersKdV mapping, Nuclear Physics B 740 [PM] (2006) 243270;
A. F. Dimakis and F. Muller-Hoissen, Rep. Math. Phys. 46 (2000) 203; Non-Commutative Kortewegde-Vries equation, hep-th 0007074;
A. Connes, Non-commutative geometry, Academic Press (1994);
B. A. Kupershmidt, Phys. Lett. A 102, 213 (1984);
M. H. Tlili AFST 6e srie, Tome 9, No 3 (2000), P. 551-564;
Strachan, I.A.B., The Moyal bracket and the dispersionless limit of the KP hierarchy, J. Phys. A. 20 (1995) 1967-1975;
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);
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);
O. Babelon, D. Bernard, M. Talon, Introduction to Classical Integrable System Cambridge University Press (2003) and references therein;
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;
Dai Zheng-De, Jiang Mu-Rung, Dai Qing-Yun, Li Shao-Lin; Chin.Phys.Lett. Vol.23, No 5 (2006)1065.
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