On different integrable systems sharing the same nondynamical r-matrix
نویسندگان
چکیده
منابع مشابه
The nondynamical r-matrix structure for the elliptic An−1 Calogero-Moser model
In this paper, we construct a new Lax operator for the elliptic An−1 Calogero-Moser model with general n(2 ≤ n) from the classical dynamical twisting, in which the corresponding r-matrix is purely numeric (nondynamical one). The nondynamical r-matrix structure of this Lax operator is obtained, which is elliptic Zn-symmetric r-matrix. Mathematics Subject Classification : 70F10 , 70H33 , 81U10.
متن کاملThe Nondynamical R-matrix Structure of the Elliptic Ruijsenaars-schneider Model with N=2
We demonstrate that in a certain gauge the elliptic Ruijsenaars-Shneider model with N=2 admits a nondynamical r-matrix structure and the corresponding classical r-matrix is the same as that of its non-relativistic counterpart (Calogero-Moser model ) in the same gauge.The relation between our (classical) Lax operator and the Lax operator given by Ruijsenaars is also obtained. Mathematics Subject...
متن کاملThe nondynamical r-matrix structure of the elliptic Calogero-Moser Model
The elliptic Calogero-Moser (CM) model[1-4] is the system of N one-dimensional particles interacting by two-particle potential of the elliptic type. It is well-known that the CM model is completely integrable[18]. The Lax operator of this system , which is the most effective way to construct the complete set of integrals of motion, was found by Krichever[6] . The classical r-matrix structure of...
متن کاملThe dynamical twisting and nondynamical r-matrix structure for the elliptic Ruijsenaars-Schneider model
From the dynamical twisting of the classical r-matrix, we obtain a new Lax operator for the elliptic Ruijsenaars-Schneider model (cf. Ruisenaars’). The corresponding r-matrix is shown to be the classical Zn-symmetric elliptic r-matrix, which is the same as that obtained in the study of the nonrelativistic version—the An−1 Calogero-Moser model givened by us. Mathematics Subject Classification : ...
متن کاملThe dynamical twisting and nondynamical r-matrix structure of elliptic Ruijsenaars-Schneider model
From the dynamical twisting of the classical r-matrix, we obtain a new Lax operator for the elliptic Ruijsenaars-Schneider model (cf. Ruijsenaars’). The corresponding r-matrix is shown to be the classical Zn-symmetric elliptic r-matrix, which is the same as that obtained in the study of the nonrelativistic version—the An−1 Calogero-Moser model. Mathematics Subject Classification : 70F10 , 70H33...
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ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 1998
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.532253