  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.
