On Different Integrable Systems Sharing the Same Nondynamical R-Matrix

Authors

Zhijun Qiao, The University of Texas Rio Grande ValleyFollow
Walter Strampp, Universitat-GH Kassel

Document Type

Article

Publication Date

5-1998

Abstract

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.

Comments

© 1998 American Institute of Physics. Original published version available at https://doi.org/10.1063/1.532253

Recommended Citation

Qiao, Zhijun, and Walter Strampp. 1998. “On Different Integrable Systems Sharing the Same Nondynamical R-Matrix.” Journal of Mathematical Physics 39 (6): 3271–79. https://doi.org/10.1063/1.532253.

First Page

3271

Last Page

3279

Publication Title

Journal of Mathematical Physics

DOI

10.1063/1.532253