For the two dimensional Toda equations corresponding to the Kac-Moody algebras C_l⁽¹⁾ and D_l+1⁽²⁾, the Darboux transformations with special choice of spectral parameters are constructed so that the degree of these Darboux transformations is the half of that for usual Darboux transformations and the derived solutions become simpler. These Darboux transformations for a Lax pair are constructed from real solutions of itself or a slightly different Lax pair corresponding to the same Toda equation, depending on the parity of l. Exact solutions of these Toda equations are presented by simplifying the results derived from the Darboux transformations.

Full text [PDF File] (229 KB)