Bi-Hamiltonian structure of the extended noncommutative Toda hierarchy |
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Authors: | Chuanzhong Li Tao Song |
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Institution: | Department of Mathematics, Ningbo University Ningbo, 315211, Zhejiang, P. R. China |
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Abstract: | The noncommutative Toda hierarchy is studied with the help of Moyal deformation by a reduction on the non-commutative two dimensional Toda hierarchy. Further we generalize the noncommutative Toda hierarchy to the extended noncommutative Toda hierarchy. To survey on its integrability, we construct the bi-Hamiltonian structure and noncommutative conserved densities of the extended noncommutative Toda hierarchy by means of the R-matrix formalism. This extended noncommutative Toda hierarchy can be reduced to the extended multicomponent Toda hierarchy, extended ZN?-Toda hierarchy, extended Toda hierarchy respectively by reductions on Lie algebras. |
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Keywords: | noncommutative Toda hierarchy extended noncommutative Toda hierarchy bi-Hamiltonian structure |
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