Separation of variables for the Clebsch model: so(4) spectral/separation curves

Abstract

In the present paper we construct symmetric separation of variables (SoV) for the anisotropic Clebsch model for which both curves of separation coincide with spectral curve K of its so(4)-valued Lax matrix. We explicitly construct coordinates and momenta of separation, Abel-type quadratures and reconstruction formulae for the presented new SoV. The found SoV is the first example of SoV for integrable systems with generic so(n)-valued Lax matrices when all curves of separation coincide with a spectral curve of the corresponding so(n)-valued Lax matrix and n > 3.