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

• 来源期刊: 理论物理通讯（英文版）
• 年，卷（期）: 2017,（4）
• 页码范围: 396-406
• 页数: 11页
• 语种: 英文
• DOI: 10.1088/0253-6102/67/4/396

摘要

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.