Simplified basic equations describing ionization waves excited in the positive columns of glow discharges are numerically solved as an initial value problem under a certain boundary condition. The nonlinear dispersion relation with the finite wave amplitude in the basic equations is also calculated. The frequency decrease with increasing wave amplitude is obtained from the relation. We can predict the evolution of envelope solitons by evaluating the coefficients of the nonlinear Schro¨dinger equation from the backward wave property and the frequency decrease. By applying an envelope solutions as an initial value, the soliton propagates by keeping its initial waveform in contrast to spreading the width of an arbitrary wave packet with a small amplitude.