On Hamiltonian operators in differential algebras

TL;DR

This paper advances an algebraic method for identifying Hamiltonian operators in differential algebras, providing a systematic way suitable for computer calculations and illustrating it with a simple example.

Contribution

It develops a new algebraic framework for Hamiltonian operators in differential algebras, including a defining system of equations for computational purposes.

Findings

Presented a defining system of equations for Hamiltonian operators.

Demonstrated the approach with a simple illustrative example.

Enhanced the algebraic techniques for Hamiltonian systems in PDEs.

Abstract

Before we proposed an algebraic technics for the Hamiltonian approach to the evolution systems of partial differential equations, including systems with constraints. Here we further develop this approach and present the defining system of equations (suitable for the computer calculations), characterizing the Hamiltonian operators of the given form. We illustrate our technics by a simple example.