On New Hamiltonian Structures of Two Integrable Couplings
In this paper, we present new Hamiltonian operators for the integrable couplings of the Ablowitz–Kaup–Newell–Segur hierarchy and the Kaup–Newell hierarchy. The corresponding Hamiltonians allow nontrivial degeneration. Multi-Hamiltonian structures are investigated. The involutive property is proven f...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-10-01
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| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/14/11/2259 |
| _version_ | 1797466368847642624 |
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| author | Yu Liu Jin Liu Da-jun Zhang |
| author_facet | Yu Liu Jin Liu Da-jun Zhang |
| author_sort | Yu Liu |
| collection | DOAJ |
| description | In this paper, we present new Hamiltonian operators for the integrable couplings of the Ablowitz–Kaup–Newell–Segur hierarchy and the Kaup–Newell hierarchy. The corresponding Hamiltonians allow nontrivial degeneration. Multi-Hamiltonian structures are investigated. The involutive property is proven for the new and known Hamiltonians with respect to the two Poisson brackets defined by the new and known Hamiltonian operators. |
| first_indexed | 2024-03-09T18:35:58Z |
| format | Article |
| id | doaj.art-31301345f4f84eb8afad5219a28902e2 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T18:35:58Z |
| publishDate | 2022-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-31301345f4f84eb8afad5219a28902e22023-11-24T07:07:25ZengMDPI AGSymmetry2073-89942022-10-011411225910.3390/sym14112259On New Hamiltonian Structures of Two Integrable CouplingsYu Liu0Jin Liu1Da-jun Zhang2Department of Mathematics, Shanghai University, Shanghai 200444, ChinaDepartment of Mathematics, Shanghai University, Shanghai 200444, ChinaDepartment of Mathematics, Shanghai University, Shanghai 200444, ChinaIn this paper, we present new Hamiltonian operators for the integrable couplings of the Ablowitz–Kaup–Newell–Segur hierarchy and the Kaup–Newell hierarchy. The corresponding Hamiltonians allow nontrivial degeneration. Multi-Hamiltonian structures are investigated. The involutive property is proven for the new and known Hamiltonians with respect to the two Poisson brackets defined by the new and known Hamiltonian operators.https://www.mdpi.com/2073-8994/14/11/2259integrable couplingHamiltonian structureHamiltonianAblowitz–Kaup–Newell–Segur hierarchyKaup–Newell hierarchy |
| spellingShingle | Yu Liu Jin Liu Da-jun Zhang On New Hamiltonian Structures of Two Integrable Couplings Symmetry integrable coupling Hamiltonian structure Hamiltonian Ablowitz–Kaup–Newell–Segur hierarchy Kaup–Newell hierarchy |
| title | On New Hamiltonian Structures of Two Integrable Couplings |
| title_full | On New Hamiltonian Structures of Two Integrable Couplings |
| title_fullStr | On New Hamiltonian Structures of Two Integrable Couplings |
| title_full_unstemmed | On New Hamiltonian Structures of Two Integrable Couplings |
| title_short | On New Hamiltonian Structures of Two Integrable Couplings |
| title_sort | on new hamiltonian structures of two integrable couplings |
| topic | integrable coupling Hamiltonian structure Hamiltonian Ablowitz–Kaup–Newell–Segur hierarchy Kaup–Newell hierarchy |
| url | https://www.mdpi.com/2073-8994/14/11/2259 |
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