  We consider a wide class of nonlinear canonical quantum systems described by
a one-particle Schroedinger 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 to a nonlinear Schroedinger equation with a real nonlinearity. As an
application of this theory we consider a few already studied Schroedinger
equations as that containing the nonlinearity introduced by the
exclusion-inclusion principle, the Doebner-Goldin equation and others.
  PACS numbers: 03.65.-w, 11.15.-q
