Asymmetric variable separation for the Clebsch model

In the present talk we present our result on separation of variables (SoV) for the Clebsch model.
In particular, we report on the development of two methods in the variable separation theory:

• the method of the differential separability conditions;
• the method of the vector fields $Z$.

Using these two methods we construct an asymmetric variable separation for the Clebsch model. Our SoV is unusual: it is characterized by two different curves of separati on. We explicitly construct coordinates and momenta of separation, the reconstruction formulae and the Abel-type quadratures for the Clebsch system. The solution of the non-standard Abel-Jacobi inversion problem is briefly discussed.