Integrable counterparts of the D-Kaup–Newell soliton hierarchy

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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.