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Two families of Liouville integrable lattice equations |
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| Authors: | Xin-Yue Li Yu-Xia LiHong-Xiang Yang |
| Institution: | a College of Science, Shandong University of Science and Technology, Qingdao 266510, PR China b Key Laboratory for Robot and Intelligent Technology of Shandong Province, Qingdao 266510, PR China c Department of Information Science and Technology, Taishan College, Taian 271021, PR China |
| Abstract: | By virtue of zero curvature representations, we are successful to generate the Lax representations of two hierarchies of discrete lattice equations respectively, which are derived from two new and interesting 3 × 3 matrix spectral problems. Moreover, by using the trace identity, the bi-Hamiltonian structures of the above systems are given, and it is shown that they are integrable in the Liouville sense. Finally, infinitely many conservation laws for the second hierarchy of lattice equations are given by a direct method. |
| Keywords: | Three-by-three matrix spectral problem Discrete zero-curvature representation Discrete Hamiltonian structure Conservation laws |
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