  The integrable open-boundary conditions for the Bariev model of three coupled
one-dimensional XY spin chains are studied in the framework of the boundary
quantum inverse scattering method. Three kinds of diagonal boundary K-matrices
leading to nine classes of possible choices of boundary fields are found and
the corresponding integrable boundary terms are presented explicitly. The
boundary Hamiltonian is solved by using the coordinate Bethe ansatz technique
and the Bethe ansatz equations are derived.
