Connections via Baecklund transformations among different non-linear
evolution equations are investigated aiming to compare corresponding Abelian
and non Abelian results. Specifically, links, via Baecklund transformations,
connecting Burgers and KdV-type hierarchies of nonlinear evolution equations
are studied. Crucial differences as well as notable similarities between
Baecklund charts in the case of the Burgers - heat equation, on one side and
KdV -type equations are considered. The Baecklund charts constructed in [16]
and [17], respectively, to connect Burgers and KdV-type hierarchies of operator
nonlinear evolution equations show that the structures, in the non-commutative
cases, are richer than the corresponding commutative ones.Comment: 18 page
