Classification of 1+0 two-dimensional Hamiltonian operators

TL;DR

This paper provides a comprehensive classification of two-dimensional Hamiltonian operators composed of first-order operators and Poisson tensors, covering both degenerate and non-degenerate cases in two and three components.

Contribution

It offers the first complete classification of such Hamiltonian operators in two and three components, including degenerate and non-degenerate cases.

Findings

Classification results for 2 and 3 component operators

Analysis of degenerate and non-degenerate cases

Framework for understanding Hamiltonian operators in 2D

Abstract

In this paper, we study Hamiltonian operators which are sum of a first order operator and of a Poisson tensor, in two spatial independent variables. In particular, a complete classification of these operators is presented in two and three components, analyzing both the cases of degenerate and non degenerate leading coefficients.