  A special class of multicomponent NLS equations, generalizing the vector NLS
and related to the {\bf BD.I}-type symmetric are shown to be integrable through
the inverse scattering method (ISM). The corresponding fundamental analytic
solutions are constructing thus reducing the inverse scattering problem to a
Riemann-Hilbert problem. We introduce the minimal sets of scattering data
$\mathfrak{T}$ which determines uniquely the scattering matrix and the
potential $Q$ of the Lax operator. The elements of $\mathfrak{T}$ can be viewed
as the expansion coefficients of $Q$ over the `squared solutions' that are
natural generalizations of the standard exponentials. Thus we demonstrate that
the mapping $\mathfrak{T} \to Q$ is a generalized Fourier transform. Special
attention is paid to two special representatives of this MNLS with
three-component and five components which describe spinor ($F=1$ and $F=2$,
respectively) Bose-Einstein condensates.
