Bargmann Type Systems for the Generalization of Toda Lattices
Under a constraint between the potentials and eigenfunctions, the nonlinearization of the Lax pairs associated with the discrete hierarchy of a generalization of the Toda lattice equation is proposed, which leads to a new symplectic map and a class of finite-dimensional Hamiltonian systems. The gene...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
|
| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/287529 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832559387252621312 |
|---|---|
| author | Fang Li Liping Lu |
| author_facet | Fang Li Liping Lu |
| author_sort | Fang Li |
| collection | DOAJ |
| description | Under a constraint between the potentials and eigenfunctions, the nonlinearization of the Lax pairs associated with the discrete hierarchy of a generalization of the Toda lattice equation is proposed, which leads to a new symplectic map and a class of finite-dimensional Hamiltonian systems. The generating function of the integrals of motion is presented, by which the symplectic map and these finite-dimensional Hamiltonian systems are further proved to be completely integrable in the Liouville sense. Finally, the representation of solutions for a lattice equation in the discrete hierarchy is obtained. |
| format | Article |
| id | doaj-art-f37f2bbf65e74b27a90db4dcb3fd5284 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-f37f2bbf65e74b27a90db4dcb3fd52842025-02-03T01:30:12ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/287529287529Bargmann Type Systems for the Generalization of Toda LatticesFang Li0Liping Lu1College of Science, Henan University of Technology, 100 Lianhua Road, Zhengzhou, Henan 450001, ChinaDepartment of Information Engineering, Henan College of Finance and Taxation, Zhengkai Road, Zhengzhou, Henan 451464, ChinaUnder a constraint between the potentials and eigenfunctions, the nonlinearization of the Lax pairs associated with the discrete hierarchy of a generalization of the Toda lattice equation is proposed, which leads to a new symplectic map and a class of finite-dimensional Hamiltonian systems. The generating function of the integrals of motion is presented, by which the symplectic map and these finite-dimensional Hamiltonian systems are further proved to be completely integrable in the Liouville sense. Finally, the representation of solutions for a lattice equation in the discrete hierarchy is obtained.http://dx.doi.org/10.1155/2014/287529 |
| spellingShingle | Fang Li Liping Lu Bargmann Type Systems for the Generalization of Toda Lattices Journal of Applied Mathematics |
| title | Bargmann Type Systems for the Generalization of Toda Lattices |
| title_full | Bargmann Type Systems for the Generalization of Toda Lattices |
| title_fullStr | Bargmann Type Systems for the Generalization of Toda Lattices |
| title_full_unstemmed | Bargmann Type Systems for the Generalization of Toda Lattices |
| title_short | Bargmann Type Systems for the Generalization of Toda Lattices |
| title_sort | bargmann type systems for the generalization of toda lattices |
| url | http://dx.doi.org/10.1155/2014/287529 |
| work_keys_str_mv | AT fangli bargmanntypesystemsforthegeneralizationoftodalattices AT lipinglu bargmanntypesystemsforthegeneralizationoftodalattices |