School of Mathematical and Statistical Sciences Faculty Publications and Presentations

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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 pair 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.


© 1998 American Institute of Physics. Original published version available at

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Journal of Mathematical Physics



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Mathematics Commons



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