Separation of Variables, QuasiTrigonometric rMatrices and Generalized Gaudin Models
Abstract
We construct two new oneparametric families of separated variables for the classical Laxintegrable Hamiltonian systems governed by a oneparametric family of nonskewsymmetric, nondynamical $\mathfrak{gl}(2)\otimes \mathfrak{gl}(2)$valued quasitrigonometric classical $r$matrices. We show that for all but one classical $r$matrices in the considered oneparametric 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 $N=2$ quasitrigonometric Gaudin models in an external magnetic field.
 Publication:

SIGMA
 Pub Date:
 July 2021
 DOI:
 10.3842/SIGMA.2021.069
 arXiv:
 arXiv:2107.08376
 Bibcode:
 2021SIGMA..17..069S
 Keywords:

 integrable systems; separation of variables; classical rmatrices;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems;
 Mathematical Physics
 EPrint:
 SIGMA 17 (2021), 069, 21 pages