In this paper, we study the solution behavior of two coupled nonlinear Schrödinger equations (CNLS) in the critical case, where one equation includes gain, while the other includes losses. Next, we present two numerical methods for solving the CNLS equations, for which we have made a comparison. These numerical experiments permit to illustrate other theoretical results proven by the authors [11]. We also obtain several numerical results for different non-linearities and investigate on the value of the blow up time relatively to some parameters.