A Few Discrete Lattice Systems and Their Hamiltonian Structures, Conservation Laws

作者：Guo, Xiu-Rong^*; Zhang, Yu-Feng^*; Zhang, Xiang-Zhi; Yue, Rong

来源：Communications in Theoretical Physics, 2017, 67(4): 396-406.

DOI：10.1088/0253-6102/67/4/396

• discrete lattice system
• r-matrix
• Hamiltonian structure

With the help of three shift operators and r-matrix theory, a few discrete lattice systems are obtained which can be reduced to the well-known Toda lattice equation with a constraint whose Hamiltonian structures are generated by Poisson tensors of some induced Lie Poisson bracket. The recursion operators of these lattice systems are constructed starting from Lax representations. Finally, reducing the given shift operators to get a simpler one and its expanding shift operators, we produce a lattice system with three vector fields whose recursion operator is given. Furthermore, we reduce the lattice system with three vector fields to get a lattice system whose Lax pair and conservation laws are obtained, respectively.

• 出版日期2017-4
• 单位中国矿业大学（北京）; 山东科技大学