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

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2021
• ISSN: 1815-0659
• Main Author: Skrypnyk, Taras
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2021
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/211354
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Separation of Variables, Quasi-Trigonometric -Matrices and Generalized Gaudin Models. Taras Skrypnyk. SIGMA 17 (2021), 069, 21 pages

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