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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
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.
Received: July 9, 2024; in final form September 4, 2024; Published online September 10, 2024
Citation:
Xin Hu, Matteo Casati, “Multidimensional Nonhomogeneous Quasi-Linear Systems and Their Hamiltonian Structure”, SIGMA, 20 (2024), 081, 17 pp.
Linking options:
https://www.mathnet.ru/eng/sigma2083 https://www.mathnet.ru/eng/sigma/v20/p81
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Abstract page: | 12 | Full-text PDF : | 8 | References: | 5 |
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