Separation of variables for the Clebsch model: so(4) spectral/separation curves - Skrypnyk, Taras (Journal of Geometry and Physics, 2025)
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.