This article is cited in 1 paper

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.

MSC: 37K10, 37K25

Received: July 9, 2024; in final form September 4, 2024; Published online September 10, 2024

Language: English

DOI: 10.3842/SIGMA.2024.081

ArXiv: 2401.10445