Nonlinear gauge transformation for a quantum system obeying an exclusion-inclusion principle

We introduce a nonlinear and noncanonical gauge transformation which allows the reduction of a complex nonlinearity, contained in a Schrödinger equation, into a real one. This Schrödinger equation describes a canonical system, whose kinetics is governed by a generalized Exclusion-Inclusion Principle. The transformation can be easily generalized and used in order to reduce complex nonlinearities into real ones for a wide class of nonlinear Schrödinger equations. We show also that, for one dimensional system and in the case of solitary waves, the above transformation coincides with the one already adopted to study the Doebner-Goldin equation.