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

作     者：郭秀荣 张玉峰 张祥芝 岳嵘 

作者机构：College of MathematicsChina University of Mining and Technology Basic CoursesShandong University of Science and Technology 

出 版 物：《Communications in Theoretical Physics》 (理论物理通讯（英文版）)

年 卷 期：2017年第67卷第4期

页      面：396-406页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Supported by the National Natural Science Foundation of China under Grant No.11371361 the Innovation Team of Jiangsu Province Hosted by China University of Mining and Technology(2014) the the Key Discipline Construction by China University of Mining and Technology under Grant No.XZD201602 the Shandong Provincial Natural Science Foundation,China under Grant Nos.ZR2016AM31,ZR2016AQ19,ZR2015EM042 the Development of Science and Technology Plan Projects of Tai An City under Grant No.2015NS1048 National Social Science Foundation of China under Grant No.13BJY026 A Project of Shandong Province Higher Educational Science and Technology Program under Grant No.J14LI58 

主　　题：discrete lattice system r-matrix Hamiltonian structure 

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.