Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1899348 | Reports on Mathematical Physics | 2013 | 16 Pages |
Abstract
W. X. Ma established theory of bi-integrable couplings to construct Hamilton structure of continuous bi-integrable couplings. In our paper, the theory of bi-integrable couplings is generalized to the discrete case. First, based on semi-direct sums of Lie subalgebra, a class of higher-dimensional 6Ã6 matrix Lie algebras is constructed. Moreover, starting from a new 6-order matrix spectral problem with a parameter, the bi-integrable couplings of the Toda lattice hierarchy was obtained from the proposed nonsemisimple higher-dimensional Lie algebras. Finally, the obtained discrete bi-integrable coupling systems are all written into their bi-Hamiltonian forms by the discrete variational identity.
Keywords
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Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Xin-Yue Li, Qiu-Lan Zhao, Yu-Xia Li,