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A new matrix Lie algebra, the multicomponent Yang hierarchy and its super-integrable coupling system. (English) Zbl 1162.17027
Summary: A set of new matrix Lie algebras is constructed, which is devoted to obtaining a new loop algebra $\widetilde A_{2M}$. It follows that an isospectral problem is established. By use of Tu scheme, a Liouville integrable multi-component hierarchy of soliton equations is generated, which possesses the multi-component Hamiltonian structures. As its reduction cases, the multi-component Yang hierarchy is given. Finally, the multi-component super-integrable coupling system of Yang hierarchy is presented by enlarging matrix spectral problem.

17B80Applications of Lie algebras to integrable systems
37K30Relations of infinite-dimensional systems with algebraic structures
37K10Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies
Full Text: DOI
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