Separates variables for finite-zones sectors of  nonlinear integrable equations

Abstract:
We presented the general scheme for the separation variables in finite-zone sectors of nonlinear equations of AKNS-series. The "action-angle" variables are calculated in terms of  "roots variables" for the finite-zone sector of  NLS, Sine-Gordon, DNLS et al. equations. The geometrical aspects of the problem of separation variables are discussed.