International Journal of Sustainable and Green Energy

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Notes on the Boussinesq Integrable Hierarchy

Received: 20 November 2014    Accepted: 28 November 2014    Published: 15 December 2014
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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.

DOI 10.11648/j.ijrse.s.2015040302.14
Published in International Journal of Sustainable and Green Energy (Volume 4, Issue 3-2, May 2015)

This article belongs to the Special Issue Wind-Generated Waves, 2D Integrable KdV Hierarchies and Solitons

Page(s) 17-22
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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), 2024. Published by Science Publishing Group

Keywords

Moyal Momentum Algebra, Moyal KP Hierarchy, Non-Commutative Boussinesq Hierarchy

References
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[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;
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[11] M. H. Tlili AFST 6e srie, Tome 9, No 3 (2000), P. 551-564;
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[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;
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  • 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

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    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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    AMA 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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  • @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}
    }
    

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Author Information
  • Department of Physics, Faculty of Science, Douala University, Douala, Cameroun

  • CEPAMOQ, Douala University, Douala, Cameroun

  • LHESIR, Faculty of Science of Kenitra, Ibn Toufail University, Kenitra, Morocco

  • LHESIR, Faculty of Science of Kenitra, Ibn Toufail University, Kenitra, Morocco; ENSAH, Mohammed First University, Al Hoceima, Morocco

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