Integrable counterparts of the D-Kaup-Newell soliton hierarchy

Two integrable counterparts of the D-Kaup-Newell soliton hierarchy are constructed from a matrix spectral problem associated with the three dimensional special orthogonal Lie algebra so(3,R). An application of the trace identity presents Hamiltonian or quasi-Hamiltonian structures of the resulting counterpart soliton hierarchies, thereby showing their Liouville integrability, i.e., the existence of infinitely many commuting symmetries and conserved densities. The involved Hamiltonian and quasi-Hamiltonian properties are shown by computer algebra systems.