Volume 4, Issue 3-2, May 2015, Page: 10-16
Note on the 3-Graded Modified Classical Yang-Baxter Equations and Integrable Systems
Mahmoud Akdi, LHESIR, Faculty of Science of Kenitra, Ibn Toufail University, Kenitra, Morocco
Amina Boulahoual, LHESIR, Faculty of Science of Kenitra, Ibn Toufail University, Kenitra, Morocco
Moulay Brahim Sedra, LHESIR, Faculty of Science of Kenitra, Ibn Toufail University, Kenitra, Morocco; ENSAH, Mohammed First University, Al Hoceima, Morocco
Received: Nov. 1, 2014;       Accepted: Nov. 5, 2014;       Published: Nov. 11, 2014
DOI: 10.11648/j.ijrse.s.2015040302.13      View  2626      Downloads  98
Abstract
The 6=3×2 huge Lie algebra Ξ of all local and non-local differential operators on a circle is applied to the standard Adler-Kostant-Symes (AKS) R-bracket scheme. It is shown in particular that there exist three additional Lie structures, associated to three graded modified classical Yang-Baxter (GMCYB) equations. As we know from the standard case, these structures can be used to classify in a more consistent way a wide class of integrable systems. Other algebraic properties are also presented.
Keywords
Huge Lie Algebra, Graded Modified Classical Yang-Baxter Equations, Integrable Hamiltonian Systems
To cite this article
Mahmoud Akdi, Amina Boulahoual, Moulay Brahim Sedra, Note on the 3-Graded Modified Classical Yang-Baxter Equations and Integrable Systems, 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. 10-16. doi: 10.11648/j.ijrse.s.2015040302.13
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