On different integrable systems sharing the same nondynamical r-matrix

In a recent paper [Zhijun Qiao and Ruguang Zhou, Phys. Lett. A 235, 35 (1997)], the amazing fact was reported that a discrete and a continuous integrable system share the same r-matrix with the interesting property of being nondynamical. Now, we present three further pairs of different continuous integrable systems sharing the same r-matrix again being nondynamical. The first pair is the finite-dimensional constrained system (FDCS) of the famous AKNS hierarchy and the Dirac hierarchy; the second pair is the FDCS of the well-known geodesic flows on the ellipsoid and the Heisenberg spin chain hierarchy; and the third Flair is the FDCS of one hierarchy studied by Xianguo Geng [Phys. Lett. A 162,:375 (1992)] and another hierarchy proposed by Zhijun Qiao [Phys. Lett. A 192, 316 (1994)]. All those FDCSs possess Lax representations and from the viewpoint of r-matrix can be shown to be completely integrable in Liouville's sense. (C) 1998 American Institute of Physics.