On the Bäcklund transformation for the Gel'fand-Dickey equations

We study the Bäcklund transformation of the Gel'fand-Dickey equations, and in particular how the factorization ofn ^th order differential operators leads to Lax type equations for first order operators, generalizing work of Adler and Moser 1]. In a similar fashion we study the Toda equations.Part of this work was done under the auspices of the SFB program of the Mathematical Institute of Bonn University, and the other part was done under NSF contract No. MCS 79-01998