Integrable Systems with Pairwise Interactions and Functional Equations
  A new ansatz is presented for a Lax pair describing systems of particles on the line interacting via (possibly nonsymmetric) pairwise forces. Particular cases of this yield the known Lax pairs for the Calogero-Moser and Toda systems, as well as their relativistic generalisations. The ansatz leads to a system of functional equations. Several new functional equations are described and the general analytic solution to some of these is given. New integrable systems are described. 
H. W. Braden, V. M. Buchstaber