Abstract
We present a spectral problem, based on the three-dimensional real special orthogonal Lie algebra
$\textrm {so}(3,\mathbb {R})$
so
(
3
,
R
)
, and construct a hierarchy of commuting bi-Hamiltonian soliton equations by zero curvature equations associated with the spectral problem. An illustrative example of soliton equations is computed, together with its associated bi-Hamiltonian structure.