LAUSR

Abstract In the present paper we consider a problem of separation of variables for Lax-integrable hamiltonian system generated by general non-skew-symmetric g l ( 2 ) ⊗ g l ( 2 ) -valued classical r -matrix r ( u , v ) with spectral parameters. We specify the general separability condition of Dubrovin and Skrypnyk (2018) on the components of the r -matrix and consider two new classes of examples of classical non-skew-symmetric r -matrices r ( u , v ) for which the separability condition is satisfied and the whole construction produces a complete set of canonical coordinates. For each of these r -matrices we consider in details the corresponding classical Gaudin-type models with N spins. In the case N = 2 we explicitly find coordinates and momenta of separation, reconstruction formulae and Abel–Jacobi quadratures. Some potential physical applications of the considered models are discussed.