Multidimensional Nonhomogeneous Quasi-Linear Systems and Their Hamiltonian Structure
Exactly Solvable and Integrable Systems
2024-09-11 v3 Mathematical Physics
math.MP
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
Cite
@article{arxiv.2401.10445,
title = {Multidimensional Nonhomogeneous Quasi-Linear Systems and Their Hamiltonian Structure},
author = {Xin Hu and Matteo Casati},
journal= {arXiv preprint arXiv:2401.10445},
year = {2024}
}