Three Graded Modified Classical Yang-Baxter Equations and Integrable Systems

E. H. Saidi; M. B. Sedra

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Three Graded Modified Classical Yang-Baxter Equations and Integrable Systems

E. H. Saidi·M. B. Sedra

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Abstract

The $6 = 3\times 2$ 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 sckeme. 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 consitent way a wide class of integrable systems. Other algebraic properties are also presented.

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BibTeX RIS

E. H. Saidi, M. B. Sedra. 1997-08-11. Three Graded Modified Classical Yang-Baxter Equations and Integrable Systems. https://arxiv.org/abs/solv-int/9708003

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