  We further develop the approach to many-body systems based on finding
conditions of existence of meromorphic solutions to certain linear partial
differential and difference equations which serve as auxiliary linear problems
for nonlinear integrable equations such as KP, BKP, CKP and different versions
of the Toda lattice. These conditions imply equations of the time evolution for
poles of singular solutions to the nonlinear equations which are equations of
motion for integrable many-body systems of Calogero-Moser and
Ruijsenaars-Schneider type. A new many-body system is introduced, which governs
dynamics of poles of elliptic solutions to the Toda lattice of type B.
