One-dimensional equations are derived that describe the hydrodynamic and electrodynamic properties of a plasma created through gas ionization by a short intense laser pulse. Different approaches (in particular, the particle-in-cell method) are used to show that, with ionization processes included, the excitation of a wakefield by an intense laser pulse can be described by the method of slowly varying amplitudes. It is shown that ionization processes enhance the wakefield excited by a moderate-intensity laser by about 10% in the case of a linearly polarized laser and by about 50% in the case of a circularly polarized laser. Ionization processes in light gases irradiated with high-intensity laser pulses have essentially no effect on the wakefield during the resonant excitation of a plasma wave by the ponderomotive force and play a governing role far from the resonance.