On Separation of Variables for Integrable Equations of Soliton Type

We propose a general scheme for separation of variables in the integrable Hamiltonian systems on orbits of the loop algebra $\mathfrak{s}\mathfrak{l}(2,\mathbb{C})\times \mathcal{P}(\lambda ,{\lambda }^{-1})$. In particular, we illustrate the scheme by application to modified Korteweg–de Vries (MKdV), sin(sinh)-Gordon, nonlinear Schr"odinger, and Heisenberg magnetic equations.