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.