Cole-Hopf-like transformation for Schrodinger equations containing complex nonlinearities

We consider systems which conserve the particle number and-are described by Schrodinger 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.