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ЖУРНАЛЫ // Symmetry, Integrability and Geometry: Methods and Applications // Архив

SIGMA, 2021, том 17, 069, 21 стр. (Mi sigma1751)

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

Аннотация: 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.

Ключевые слова: integrable systems, separation of variables, classical $r$-matrices.

MSC: 14H70, 17B80, 37J35

Поступила: 29 марта 2021 г.; в окончательном варианте 7 июля 2021 г.; опубликована 18 июля 2021 г.

Язык публикации: английский

DOI: 10.3842/SIGMA.2021.069



Реферативные базы данных:
ArXiv: 2107.?????


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