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

作　　者：郭秀荣 张玉峰 张祥芝 岳嵘 

机构地区：[1]College of Mathematics,China University of Mining and Technology [2]Basic Courses,Shandong University of Science and Technology

出　　处：《Communications in Theoretical Physics》2017年第4期396-406,共11页理论物理通讯（英文版）

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

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.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.

关 键 词：discrete lattice system R-MATRIX Hamiltonian structure 

分 类 号：O151.21[理学—数学] O177[理学—基础数学]