A counterpart of the WKI soliton hierarchy associated with so(3,R)

TL;DR

This paper introduces a new integrable hierarchy related to the WKI soliton hierarchy, associated with the Lie algebra so(3,R), using zero curvature formulation and trace identities.

Contribution

It constructs a novel soliton hierarchy linked to so(3,R) and establishes its Hamiltonian structures for Liouville integrability.

Findings

Defines a spectral matrix similar to WKI's

Derives Hamiltonian structures via trace identity

Shows Liouville integrability of the hierarchy

Abstract

A counterpart of the Wadati-Konno-Ichikawa (WKI) soliton hierarchy, associated with so(3,R), is presented through the zero curvature formulation. Its spectral matrix is defined by the same linear combination of basis vectors as the WKI one, and its Hamiltonian structures yielding Liouville integrability are furnished by the trace identity.