  We discuss the concept of Lax-Darboux scheme and illustrate it on well known
examples associated with the Nonlinear Schrodinger (NLS) equation. We explore
the Darboux links of the NLS hierarchy with the hierarchy of Heisenberg model,
principal chiral field model as well as with differential-difference integrable
systems (including the Toda lattice and differential-difference Heisenberg
chain) and integrable partial difference systems. We show that there exists a
transformation which formally diagonalises all elements of the Lax-Darboux
scheme simultaneously. It provides us with generating functions of local
conservation laws for all integrable systems obtained. We discuss the relations
between conservation laws for systems belonging to the Lax-Darboux scheme.
