  A special class of integrable nonlinear differential equations related to
A.III-type symmetric spaces and having additional reductions are analyzed via
the inverse scattering method (ISM). Using the dressing method we construct two
classes of soliton solutions associated with the Lax operator. Next, by using
the Wronskian relations, the mapping between the potential and the minimal sets
of scattering data is constructed. Furthermore, completeness relations for the
'squared solutions' (generalized exponentials) are derived. Next, expansions of
the potential and its variation are obtained. This demonstrates that the
interpretation of the inverse scattering method as a generalized Fourier
transform holds true. Finally, the Hamiltonian structures of these generalized
multi-component Heisenberg ferromagnetic (MHF) type integrable models on
A.III-type symmetric spaces are briefly analyzed.
