Bi-Integrable Couplings of a New Soliton Hierarchy Associated with SO(4)

Based on the six-dimensional real special orthogonal Lie algebra SO(4), a new Lax integrable hierarchy is obtained by constructing an isospectral problem. Furthermore, we construct bi-integrable couplings for this hierarchy from the enlarged matrix spectral problems and the enlarged zero curvature equations. Hamiltonian structures of the obtained bi-integrable couplings are constructed by the variational identity