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Symmetry, Integrability and Geometry: Methods and Applications, 2024, Volume 20, 081, 17 pp.
DOI: https://doi.org/10.3842/SIGMA.2024.081 (Mi sigma2083) 		 
Multidimensional Nonhomogeneous Quasi-Linear Systems and Their Hamiltonian Structure

Xin Hu, Matteo Casati

School of Mathematics and Statistics, Ningbo University, Ningbo 315211, P.R. China
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DOI: https://doi.org/10.3842/SIGMA.2024.081
Abstract: 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-components systems of hydrodynamic type and of a real reduction of the 3-waves system.
Keywords: Hamiltonian structures, quasilinear systems, non-homogeneous operators.
Funding agency Grant number
National Natural Science Foundation of China 12101341
This work was sponsored by the National Science Foundation of China (grant no. 12101341), Ningbo City Yongjiang Innovative Talent Program and Ningbo University Talent Introduction and Resarch Initiation Fund.
Received: July 9, 2024; in final form September 4, 2024; Published online September 10, 2024
Document Type: Article
MSC: 37K10, 37K25
Language: English
Citation: Xin Hu, Matteo Casati, “Multidimensional Nonhomogeneous Quasi-Linear Systems and Their Hamiltonian Structure”, SIGMA, 20 (2024), 081, 17 pp.
Citation in format AMSBIB
\Bibitem{HuCas24}
\by Xin~Hu, Matteo~Casati
\paper Multidimensional Nonhomogeneous Quasi-Linear Systems and Their Hamiltonian Structure
\jour SIGMA
\yr 2024
\vol 20
\papernumber 081
\totalpages 17
\mathnet{http://mi.mathnet.ru/sigma2083}
\crossref{https://doi.org/10.3842/SIGMA.2024.081}
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