Multidimensional Nonhomogeneous Quasi-Linear Systems and Their Hamiltonian Structure
In this paper, we investigate multidimensional first-order quasi-linear systems and find necessary conditions for them to admit Hamiltonian formulation. The insufficiency of the conditions is related to the Poisson cohomology of the admissible Hamiltonian operators. We present in detail the examples...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2024 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2024
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/212615 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Multidimensional Nonhomogeneous Quasi-Linear Systems and Their Hamiltonian Structure. Xin Hu and Matteo Casati. SIGMA 20 (2024), 081, 17 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862653588442972160 |
|---|---|
| author | Hu, Xin Casati, Matteo |
| author_facet | Hu, Xin Casati, Matteo |
| citation_txt | Multidimensional Nonhomogeneous Quasi-Linear Systems and Their Hamiltonian Structure. Xin Hu and Matteo Casati. SIGMA 20 (2024), 081, 17 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | In this paper, we investigate multidimensional first-order quasi-linear systems and find necessary conditions for them to admit Hamiltonian formulation. The insufficiency of the conditions is related to the Poisson cohomology of the admissible Hamiltonian operators. We present in detail the examples of two-dimensional, two-component systems of hydrodynamic type and of a real reduction of the 3-wave system.
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| first_indexed | 2026-03-15T17:24:43Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-212615 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-15T17:24:43Z |
| publishDate | 2024 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Hu, Xin Casati, Matteo 2026-02-09T08:06:48Z 2024 Multidimensional Nonhomogeneous Quasi-Linear Systems and Their Hamiltonian Structure. Xin Hu and Matteo Casati. SIGMA 20 (2024), 081, 17 pages 1815-0659 2020 Mathematics Subject Classification: 37K10; 37K25 arXiv:2401.10445 https://nasplib.isofts.kiev.ua/handle/123456789/212615 https://doi.org/10.3842/SIGMA.2024.081 In this paper, we investigate multidimensional first-order quasi-linear systems and find necessary conditions for them to admit Hamiltonian formulation. The insufficiency of the conditions is related to the Poisson cohomology of the admissible Hamiltonian operators. We present in detail the examples of two-dimensional, two-component systems of hydrodynamic type and of a real reduction of the 3-wave system. This work was supported by the National Science Foundation of China (grant no. 12101341), the Ningbo City Yongjiang Innovative Talent Program, and the Ningbo University Talent Introduction and Research Initiation Fund. M.C. wishes to thank P. Vergallo and I. Marcut for the useful insights. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Multidimensional Nonhomogeneous Quasi-Linear Systems and Their Hamiltonian Structure Article published earlier |
| spellingShingle | Multidimensional Nonhomogeneous Quasi-Linear Systems and Their Hamiltonian Structure Hu, Xin Casati, Matteo |
| title | Multidimensional Nonhomogeneous Quasi-Linear Systems and Their Hamiltonian Structure |
| title_full | Multidimensional Nonhomogeneous Quasi-Linear Systems and Their Hamiltonian Structure |
| title_fullStr | Multidimensional Nonhomogeneous Quasi-Linear Systems and Their Hamiltonian Structure |
| title_full_unstemmed | Multidimensional Nonhomogeneous Quasi-Linear Systems and Their Hamiltonian Structure |
| title_short | Multidimensional Nonhomogeneous Quasi-Linear Systems and Their Hamiltonian Structure |
| title_sort | multidimensional nonhomogeneous quasi-linear systems and their hamiltonian structure |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212615 |
| work_keys_str_mv | AT huxin multidimensionalnonhomogeneousquasilinearsystemsandtheirhamiltonianstructure AT casatimatteo multidimensionalnonhomogeneousquasilinearsystemsandtheirhamiltonianstructure |