Symmetric separation of variables for trigonometric integrable models

Abstract

We study a problem of variable separation for the classical integrable hamiltonian systems possessing Lax matrices satisfying linear r-matrix algebra with skew-symmetric sl(2)⊗sl(2)-valued trigonometric r-matrix. For all such the systems we produce new symmetric variables of separation. We show that the corresponding curve of separation differs from the spectral curve of the initial Lax matrix. The example of trigonometric Clebsch model is considered in details.