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This paper presents new exact analytical solutions of a nonlinear Schrodinger equation with a cubic–quintic nonlinearity and in presence of a couple of perturbation terms. This equation describes the dynamics of soliton propagation through an optical fiber. Several solutions are found without applying the computer codes and by considering the integration constant. The solutions are bright, dark and cnoidal solitons. These solutions may have significant applications in telecommunication systems where solitons are used to codify or for the transmission of data. The method used here is very effective and powerful and can be applied to other types of nonlinear equations.