摘要
Based on semi-direct sums of Lie subalgebra G, a higher-dimensional 6 × 6 matrix Lie algebra sμ(6) is constructed. A hierarchy of integrable coupling KdV equation with three potentials is proposed, which is derived from 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 prove that the hierarchy of the resulting Hamiltonian equations is Liouville integrable discrete Hamiltonian systems.
基金
Supported by the Nature Science Foundation of Shandong Province of China under Grant No.ZR.2009GM005
the Science and Technology Plan Project of the Educational Department of Shandong Province of China under Grant No.J09LA54
the research project of "SUST Spring Bud" of Shandong University of Science and Technology of China under Grant No.2009AZZ071