Elliptic Gaudin-type model in an external magnetic field and modified algebraic Bethe ansatz

We consider the elliptic Gaudin-type model in an external magnetic field [11-13,16,15,22] associated with non-skew-symmetric elliptic r-matrix [11] defined on 4 : 1 unramified covering of the Weierstrass cubic y2 = (u + j1)(u + j2)(u + j3). We develop a modified algebraic Bethe ansatz for the considered elliptic r-matrix and for the algebra generated by the entries of the corresponding Lax operator with the aim of obtaining the spectra of the relevant Gaudin-type Hamiltonians in terms of solutions of modified Bethe equations. The applications of the obtained result to the diagonalization of the anisotropic quantum Euler top, quantum Zhukovsky-Volterrra top, quantum Steklov and Rubanovsky tops are given.(c) 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/). Funded by SCOAP3.