Bäcklund–Shlesinger transformations for Davey–Stewartson equations

It is shown that the Bäcklund explicit reversible autotransformations for the integrable Davey–Stewartson (DS) and Boiti–Leon–Pempinelli (BLP) equations exist. The scheme of construction of DS soliton solutions with the help of such transformations is suggested. The sequantial application of Bäcklund explicit reversible autotransformations makes possible to get solutions of $(1+1)$- and $(0+2)$-dimensional Toda lattice equations. The similar transformations for the analogs of DS, which are realized on the arbitrary associative algebra with unit are showed. The connection of these $(1+2)$-dimensional models with $(1+1)$-dimensional J–S systems is discussed.