The aim of this paper is to compare different ways for truncating unbounded domains for solving general nonlinear one- and two-dimensional Schrödinger equations. We propose to analyze Complex Absorbing Potentials, Perfectly Matched Layers and Absorbing Boundary Conditions. The time discretization is made by using a semi-implicit relaxation scheme which avoids any fixed point procedure. The spatial discretization involves finite element methods. We propose some numerical experiments to compare the approaches.