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The two matrix spectral problems of Ablowitz-Kaup-Newell-Segur (AKNS) andKaup-Newell (KN) types associated with so(3,R) are generalized. Thecorresponding hierarchies of generalized soliton equations are derived by thestandard procedure using the zero curvature formulation. Recursion operatorsand bi-Hamiltonian structures are explicitly constructed for the resulting twogeneralized soliton hierarchies of AKNS and KN types, which shows theirLiouville integrability.

Integrable generalizations of the two new soliton hierarchies of AKNS and KN types associated with $so(3,\mathbb{R})$