Results of numerical calculations are presented and analyzed for pulse generation and propagation in one-and two-spacial dimensions in a medium consisting of a collection of two-level atoms which are resonantly swept-excited by an impulse excitation traveling at the speed of light in the medium. The conditions imposed for the calculation in one-spacial dimension are that T1 = T2, where T1 and T2 are the single atom relaxation and dephasing times, respectively, and that the gain, g, to loss, κ , ratio g/κ >> 1 , which determines the non-linear regime for pulse evolution. In addition, we impose that T2 >> τc, where τc is the characteristic superradiance cooperation time, so that the pulse evolves from conditions appropriate for superradiant pulse generation for sufficiently small values for the propagation distance z . We report and analyze calculational results for the transient regime of pulse buildup through the asymptotic regime of large propagation distance z where the pulse generated exhibits steady-state behavior with regard to pulse area, energy and intensity profile. Additional results of computations are presented which incorporate transverse effects and diffraction using a Gaussian radial gain profile for the initial condition and under imposed conditions comparable with those of the corresponding one-spacial dimension calculations. The results of the two sets of calculations are compared and discussed. We demonstrate and give predictive requirements for swept-gain pulse evolution from the superradiant state.