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
Date:2024
Main Authors: Hu, Xin, Casati, Matteo
Format: Article
Language:English
Published: Інститут математики НАН України 2024
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
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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.
first_indexed 2026-03-15T17:24:43Z
format Article
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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.
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Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Multidimensional Nonhomogeneous Quasi-Linear Systems and Their Hamiltonian Structure
Article
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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