Closed dressing chains of D=1 and D=2 Toda lattice

Abstract

We apply the method of dressing chains to reproduction of Toda lattice in the case of D=1 and D=2. On the example of modified equations $m_{0}TL$ and $m_{1}TL$ it is shown that combination of the Darboux and Schlesinger transformations results in closed dressing chains.

15 pages