On the Integration of a Hierarchy for the Periodic Toda Lattice with a Free Term
In this article, we have explored the Toda lattice hierarchy in the class of periodic functions with a free term. We have given an effective method of constructing of the periodic Toda lattice hierarchy with a free term. We have discussed the complete integrability of the constructed systems that is based on the inverse spectral problem of an associated discrete Hill`s equation with periodic coeﬃcients. In particular, Dubrovin-type equations are derived for the time-evolution of the spectral data corresponding to the solutions of any system in the hierarchy.