Cole—Hopf like transformation for a class of coupled nonlinear Schrödinger equations

In this paper we consider a class of coupled nonlinear Schrödinger equations for the fields ψi containing complex nonlinearities, that has been obtained by requiring that the norms |ψi|2 are conserved densities. For this class of equations we introduce a Cole—Hopf like transformation, whose effect is to reduce the complex nonlinearities into real ones, this way reducing the continuity equations of the system to the standard bilinear form. Some examples are presented to illustrate the applicability of the method.