An integrable extension of a soliton hierarchy associated with so(3,ℝ) and its bi-Hamiltonian formulation

Abstract

A hierarchy of soliton equations is constructed from an extended spectral problem associated with the three-dimensional special orthogonal real Lie algebra so(3,ℝ) by means of zero curvature equations. The bi-Hamiltonian structure of this hierarchy is also presented via the trace identity.