Higher-Dimensional Lie Algebra and New Integrable Coupling of Discrete KdV Equation |
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Authors: | LI Xin-Yue and SONG Hong-Wei |
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Institution: | College of Science, Shandong University of Science and Technology, Qingdao 266510, China |
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Abstract: | Based on semi-direct sums of Lie subalgebra \tilde{G}, a higher-dimensional 6 x 6 matrix Lie algebra sμ(6) is constructed. A hierarchy of integrable coupling KdV equation with three potentials is proposed, which is derivedfrom a new discrete six-by-six matrix spectral problem. Moreover, the Hamiltonian forms is deduced for lattice equation in the resulting hierarchy by means of the discrete variational identity --- a generalized trace identity. A strong symmetry operator of the resulting hierarchy is given. Finally, we provethat the hierarchy of the resulting Hamiltonian equations is Liouville integrable discrete Hamiltonian systems. |
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Keywords: | semi-direct sums of Lie subalgebra integrable couplings discretevariational identity Liouville integrability |
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