  We give detailed description for continuous version of the classical
IRF-Vertex relation, where on the IRF side we deal with the
Calogero-Moser-Sutherland models. Our study is based on constructing
modifications of the Higgs bundles of infinite rank over elliptic curve and its
degenerations. In this way the previously predicted gauge equivalence between
L-A pairs of the Landau-Lifshitz type equations and 1+1 field theory
generalization of the Calogero-Moser-Sutherland models is described. In this
paper the ${\rm sl}_2$ case is studied. Explicit changes of variables are
obtained between the rational, trigonometric and elliptic models.
