A binary Darboux transformation for the Toda lattice

Binary Darboux transformations for the equations of the Toda lattice are constructed. Using them, broad classes of solutions are obtained: solutions on an increasing background and bound soliton solutions. The Zakharov-Shabat dressing method is considered.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdelenniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 145, pp. 34–45, 1985.