An integrable counterpart of the D-AKNS soliton hierarchy from so(3,R)so(3,R)

•Use the Lie algebra so(3,R)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.

An integrable counterpart of the D-AKNS soliton hierarchy is generated from a matrix spectral problem associated with so(3,R)so(3,R). Hamiltonian structures of the resulting counterpart soliton hierarchy are furnished by using the trace identity, which yields its Liouville integrability.