A Few Discrete Lattice Systems and Their Hamiltonian Structures,Conservation Laws
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 oper...
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| Published in | Communications in theoretical physics Vol. 67; no. 4; pp. 396 - 406 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
01.04.2017
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| Online Access | Get full text |
| ISSN | 0253-6102 |
| DOI | 10.1088/0253-6102/67/4/396 |
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| Summary: | 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. |
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| Bibliography: | 11-2592/O3 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. discrete lattice system r-matrix Hamiltonian structure |
| ISSN: | 0253-6102 |
| DOI: | 10.1088/0253-6102/67/4/396 |