Higher-Order Matrix Spectral Problems and Their Integrable Hamiltonian Hierarchies
Starting from a kind of higher-order matrix spectral problems, we generate integrable Hamiltonian hierarchies through the zero-curvature formulation. To guarantee the Liouville integrability of the obtained hierarchies, the trace identity is used to establish their Hamiltonian structures. Illuminati...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-04-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/8/1794 |
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| author | Shou-Ting Chen Wen-Xiu Ma |
| author_facet | Shou-Ting Chen Wen-Xiu Ma |
| author_sort | Shou-Ting Chen |
| collection | DOAJ |
| description | Starting from a kind of higher-order matrix spectral problems, we generate integrable Hamiltonian hierarchies through the zero-curvature formulation. To guarantee the Liouville integrability of the obtained hierarchies, the trace identity is used to establish their Hamiltonian structures. Illuminating examples of coupled nonlinear Schrödinger equations and coupled modified Korteweg–de Vries equations are worked out. |
| first_indexed | 2024-03-11T04:46:34Z |
| format | Article |
| id | doaj.art-20afb52e8b57473292a565e36f4d777e |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T04:46:34Z |
| publishDate | 2023-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-20afb52e8b57473292a565e36f4d777e2023-11-17T20:16:32ZengMDPI AGMathematics2227-73902023-04-01118179410.3390/math11081794Higher-Order Matrix Spectral Problems and Their Integrable Hamiltonian HierarchiesShou-Ting Chen0Wen-Xiu Ma1School of Mathematics and Statistics, Xuzhou University of Technology, Xuzhou 221008, ChinaDepartment of Mathematics, Zhejiang Normal University, Jinhua 321004, ChinaStarting from a kind of higher-order matrix spectral problems, we generate integrable Hamiltonian hierarchies through the zero-curvature formulation. To guarantee the Liouville integrability of the obtained hierarchies, the trace identity is used to establish their Hamiltonian structures. Illuminating examples of coupled nonlinear Schrödinger equations and coupled modified Korteweg–de Vries equations are worked out.https://www.mdpi.com/2227-7390/11/8/1794Lax pairzero-curvature equationintegrable hierarchy NLS equationsmKdV equations |
| spellingShingle | Shou-Ting Chen Wen-Xiu Ma Higher-Order Matrix Spectral Problems and Their Integrable Hamiltonian Hierarchies Mathematics Lax pair zero-curvature equation integrable hierarchy NLS equations mKdV equations |
| title | Higher-Order Matrix Spectral Problems and Their Integrable Hamiltonian Hierarchies |
| title_full | Higher-Order Matrix Spectral Problems and Their Integrable Hamiltonian Hierarchies |
| title_fullStr | Higher-Order Matrix Spectral Problems and Their Integrable Hamiltonian Hierarchies |
| title_full_unstemmed | Higher-Order Matrix Spectral Problems and Their Integrable Hamiltonian Hierarchies |
| title_short | Higher-Order Matrix Spectral Problems and Their Integrable Hamiltonian Hierarchies |
| title_sort | higher order matrix spectral problems and their integrable hamiltonian hierarchies |
| topic | Lax pair zero-curvature equation integrable hierarchy NLS equations mKdV equations |
| url | https://www.mdpi.com/2227-7390/11/8/1794 |
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