Abstract
An integrable counterpart of the D-AKNS soliton hierarchy is generated from a matrix spectral problem associated with so(3,R). Hamiltonian structures of the resulting counterpart soliton hierarchy are furnished by using the trace identity, which yields its Liouville integrability.
•Use the Lie algebra so(3,R) to generate a counterpart of the D-AKNS soliton hierarchy.•Generate Hamiltonian structures depending potentials by the trace identity.•Obtain hierarchies of independent commuting symmetries and conserved densities.