Central extensions of cotangent universal hierarchy: (2+1)-dimensional bi-Hamiltonian systems

TL;DR

This paper introduces a (2+1)-dimensional bi-Hamiltonian extension of the cotangent universal hierarchy, expanding the mathematical framework for integrable systems and providing new insights into their Hamiltonian structures.

Contribution

It constructs a novel double central extension of the cotangent universal hierarchy and demonstrates its bi-Hamiltonian property, extending previous universal hierarchy models.

Findings

The (2+1)-dimensional extension is bi-Hamiltonian.

The extension generalizes the universal hierarchy.

It provides a new central extension of the original hierarchy.

Abstract

We introduce the cotangent universal hierarchy that extends the so-called universal hierarchy (as for the latter, see e.g. arXiv:nlin/0202008, arXiv:nlin/0312043 and arXiv:nlin/0310036). Then we construct a (2+1)-dimensional double central extension of the cotangent universal hierarchy and show that this extension is bi-Hamiltonian. This yields, as a byproduct, the central extension of the original universal hierarchy.