Separation of Variables, Quasi-Trigonometric 𝑟-Matrices and Generalized Gaudin Models

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 𝖌𝔩(2)⊗𝖌𝔩(2)-valued quasi-trigonometric classical 𝑟-matrices. We show that for all but one classical 𝑟-matr...

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Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2021
1. Verfasser: Skrypnyk, Taras
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут математики НАН України 2021
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/211354
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren:Separation of Variables, Quasi-Trigonometric 𝑟-Matrices and Generalized Gaudin Models. Taras Skrypnyk. SIGMA 17 (2021), 069, 21 pages

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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Zusammenfassung: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 𝖌𝔩(2)⊗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.
ISSN:1815-0659