Nonlinear transformation for a class of gauged Schrodinger equations with complex nonlinearities

In the present contribution we consider a class of Schrodinger equations co ntaining complex nonlinearities, describing systems with conserved norm \ p si \ (2) and minimally coupled to an abelian gauge field. We introduce a no nlinear transformation which permits the linearization of the source term i n the evolution equations for the gauge field, and transforms the nonlinear Schrodinger equations into another one with real nonlinearities. We show t hat 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 as a ge neralization of the gauge transformation of third kind introduced some year s ago by other authors.