Some Classes of Solutions to the Toda Lattice Hierarchy

Abstract

We apply an analogue of the Zakharov-Shabat dressing method to obtain infinite matrix solutions to the Toda lattice hierarchy. Using an operator transformation we convert some of these into solutions in terms of integral operators and Fredholm determinants. Others are converted into a class of operator solutions to the $l$-periodic Toda hierarchy.Comment: LaTeX file, 18 pages. Results generalized and applications to the Toda equations adde