Darboux transformations and exact solutions of two-dimensionalC(1)landD(2)l+1Toda equations

Abstract

For the two-dimensional Toda equations corresponding to the Kac–Moody algebras C(1)l and D(2)l+1, the Darboux transformations which keep all the reductions of the Lax pairs are constructed. The lowest degrees of the Darboux transformations are 2l + 2 for C(1)l and 2l for D(2)l+1. Exact solutions of these Toda equations are presented in a purely algebraic way.