Generalized Bäcklund transformations for affine Toda hierarchies

The construction of generalized Backlund transformation for the $A_n$ Affine Toda hierarchy is proposed in terms gauge acting on zero curvature representation. Such based upon graded structure underlying affine algebra which induces a classification transformations. Moreover, explicit examples $su(3)$ and $su(4)$ lead to uncover interesting composition properties various types universality character gauge-Backlund method extended all equations hierarchy. property provides systematic framework construct transformations higher flow equations. Explicit example simplest $sl(3)$ presented.