Hamiltonian structure, Darboux transformation for a soliton hierarchy associated with Lie algebra so(4, C)

In this paper, we first introduce a Lie algebra of the special orthogonal group, g=so(4, C), whose elements are 4×4 trace-free, skew-symmetric complex matrices. As its application, we obtain a new soliton hierarchy which is reduced to AKNS hierarchy and present its bi-Hamiltonian structure and Liouville integrability. Furthermore, for one of the equations in the resulting hierarchy, we construct a Darboux matrix T depending on the spectral parameter λ.