  We consider systems, which conserve the particle number and are described by
Schr\"odinger equations containing complex nonlinearities. In the case of
canonical systems, we study their main symmetries and conservation laws. We
introduce a Cole-Hopf like transformation both for canonical and noncanonical
systems, which changes the evolution equation into another one containing
purely real nonlinearities, and reduces the continuity equation to the standard
form of the linear theory. This approach allows us to treat, in a unifying
scheme, a wide variety of canonical and noncanonical nonlinear systems, some of
them already known in the literature. pacs{PACS number(s): 02.30.Jr, 03.50.-z,
03.65.-w, 05.45.-a, 11.30.Na, 11.40.Dw
