In these notes, we examine a family of dissipative Schrödinger equations with cubic nonlinearity. Equations of this type are used to describe the propagation of waves in weakly nonlinear, dispersive and dissipative media. The study focuses on determining exact solutions to equations of the considered class. The general solution to this problem is given through Weierstrass elliptic functions when the parameter that characterizes the dissipation is real. Another class of exact solutions is specified within the framework of the so-called small-phase approximation.