On the bi-Hamiltonian structure of Toda and relativistic Toda lattices |
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Authors: | Yu B Suris |
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Institution: | Am Dobben 81, 28203, Bremen, Germany |
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Abstract: | We introduce a general quadratic Poisson bracket on the associative algebra equipped with non-degenerate scalar product. With the help of this bracket we obtain the interpretation of the Toda and relativistic Toda lattices as the restrictions of one and the same bi-Hamiltonian system to two different low-dimensional manifolds, which are Poisson submanifolds with respect to two brackets simultaneously. |
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