Abstract
Based on the six-dimensional real special orthogonal Lie algebra SO(4), we construct two different isospectral problems. And the two hierarchies of soliton equations from zero curvature equations can be generated. At last, we use the property of the isomorphism SU(2) ⊗ SU(2) ≅ SO(4), and obtain the relations between the hierarchy of SU(2) ⊗ SU(2) and the hierarchy of SO(4).
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