SU(3) magnet: finite-gap integration on the lowest genus curve

We consider the integrable system of isotropic SU(3) Landau-Lifshits equation as a Hamiltonian system on a coadjoint orbit of the SU(3) loop group. We connect the mentioned equation with an isotropic SU(3) magnet because it describes the mean fields of magnetic and quadrupole moments in a spin-1 lattice. For the system of isotropic SU(3) Landau-Lifshits equation we perform separation of variables in Sklyanin's manner, and integrate in the lowest finite gap where the spectral curve is elliptic.