Elliptic Solutions of the Toda Lattice with Constraint of Type B and Deformed Ruijsenaars–Schneider System

We study elliptic solutions of the recently introduced Toda lattice with constraint type B and derive equations motion for their poles. The dynamics poles is given by deformed Ruijsenaars-Schneider system. find its commutation representation in form Manakov triple properties spectral curve. By studying more general (elliptic families), we also suggest an extension system to a field theory.