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

摘要

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.