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We outline an approach to a theory of various generalizations of the elliptic Calogero—Moser (CM) and Ruijsenaars—Schneider (RS) systems based on a special inverse problem for linear operators with elliptic coefficients. Hamiltonian theory of such systems is developed with the help of universal symplectic structure proposed by D. H. Phong and the author. Canonically conjugated variables for spin generalizations of the elliptic CM and RS systems are found.

Elliptic Solutions to Difference Nonlinear Equations and Nested Bethe Ansatz Equations