Quasilinear systems of first order PDEs with nonlocal Hamiltonian structures

TL;DR

This paper investigates whether first-order quasilinear PDE systems can be formulated with Hamiltonian structures, using differential coverings to identify conditions for local and nonlocal Hamiltonian operators.

Contribution

It introduces differential-geometric conditions for representing such PDE systems with various Hamiltonian operators, expanding the understanding of Hamiltonian formulations in PDEs.

Findings

Derived conditions for Hamiltonian formulations of PDEs

Identified criteria for local and nonlocal Hamiltonian operators

Enhanced the geometric understanding of PDE Hamiltonian structures

Abstract

In this paper we wonder whether a quasilinear system of PDEs of first order admits Hamiltonian formulation with local and nonlocal operators. By using the theory of differential coverings, we find differential-geometric conditions necessary to write a given system with one of the three Hamiltonian operators investigated.