Nonlinear gauge transformation for a class of Schrِdinger equations containing complex nonlinearities

We consider a wide class of nonlinear canonical quantum systems described by a one-particle Schrِdinger equation containing a complex nonlinearity. We introduce a nonlinear unitary transformation which permits us to linearize the continuity equation. In this way we are able to obtain a new quantum system obeying a nonlinear Schrِdinger equation with a real nonlinearity. As an application of this theory we consider a few already studied Schrِdinger equations, such as that containing the nonlinearity introduced by the exclusion-inclusion principle, the Doebner-Goldin equation and other ones.