Multidimensional nonhomogeneous quasi-linear systems and their Hamiltonian structures

Author:

Xin Hu, Matteo Casati

Keyword:

Nonlinear Sciences, Exactly Solvable and Integrable Systems, Exactly Solvable and Integrable Systems (nlin.SI), Mathematical Physics (math-ph)

journal:

date:

2024-01-19 00:00:00

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 example of two-dimensional, two-components systems of hydrodynamic type.

PDF: Multidimensional nonhomogeneous quasi-linear systems and their Hamiltonian structures.pdf