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

@article{Skrypnyk2021SeparationOV, title={Separation of Variables, Quasi-Trigonometric r-Matrices and Generalized Gaudin Models}, author={Taras V. Skrypnyk}, journal={Symmetry, Integrability and Geometry: Methods and Applications}, year={2021} }

We construct two new one-parametric families of separated variables for the classical Lax-integrable Hamiltonian systems governed by a one-parametric family of nonskew-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… Expand

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