  In the present contribution we consider a class of Schroedinger equations
containing complex nonlinearities, describing systems with conserved norm
$|\psi|^2$ and minimally coupled to an abelian gauge field. We introduce a
nonlinear transformation which permits the linearization of the source term in
the evolution equations for the gauge field, and transforms the nonlinear
Schroedinger equations in another one with real nonlinearities. We show that
this transformation can be performed either on the gauge field $A_\mu$ or,
equivalently, on the matter field $\psi$. Since the transformation does not
change the quantities $|\psi|^2$ and $F_{\mu\nu}$, it can be considered a
generalization of the gauge transformation of third kind introduced some years
ago by other authors.
  Pacs numbers: 03.65.-w, 11.15.-q
