In this paper, using a suitable change of variable and applying the Adomian decomposition method to the generalized nonlinear Schr¨odinger equation, we obtain the analytical solution, taking into account the parameters such as the self-steepening factor, the second-order dispersive parameter, the third-order dispersive parameter and the nonlinear Kerr effect coefficient, for pulses that contain just a few optical cycle. The analytical solutions are plotted. Under influence of these effects, pulse did not maintain its initial shape.