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Separation of Variables, Quasi-Trigonometric $r$-Matrices and Generalized Gaudin Models
Taras Skrypnyk Bogolyubov Institute for Theoretical Physics, 14-b Metrolohichna Str., Kyiv, 03680, Ukraine
Abstract:
We construct two new one-parametric families of separated variables for the classical Lax-integrable Hamiltonian systems governed by a one-parametric family of non-skew-symmetric, non-dynamical $\mathfrak{gl}(2)\otimes \mathfrak{gl}(2)$-valued quasi-trigonometric classical $r$-matrices. We show that for all but one classical $r$-matrices in the considered one-parametric families the corresponding curves of separation differ from the standard spectral curve of the initial Lax matrix. The proposed scheme is illustrated by an example of separation of variables for $N=2$ quasi-trigonometric Gaudin models in an external magnetic field.
Keywords:
integrable systems, separation of variables, classical $r$-matrices.
Received: March 29, 2021; in final form July 7, 2021; Published online July 18, 2021
Citation:
Taras Skrypnyk, “Separation of Variables, Quasi-Trigonometric $r$-Matrices and Generalized Gaudin Models”, SIGMA, 17 (2021), 069, 21 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1751 https://www.mathnet.ru/eng/sigma/v17/p69
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Abstract page: | 60 | Full-text PDF : | 13 | References: | 6 |
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