We present a formalism and a technique for analyzing the propagation of optical signals through semiconductor traveling-wave amplifiers. The formalism retains, in particular, the spontaneous recombination term, and the newly developed technique permits analytic, real-time solutions to be obtained, so that both the transient and the steady-state regimes are characterized. This end has been achieved by iteratively applying the method of in order to solve the set of coupled differential equations that result from the formulation of the characteristics physical problem. From the real-time solutions so obtained it is also possible easily to recognize the amplitude and phase-modulation effects that occur not only in the steady state but also in the transient regime.