The fluid dynamical analysis of an electron gas has been recently reviewed and applied to the final stages of an electrical breakdown in gases at atmospheric pressure. In particular, it has been used to describe the wavelike propagation of luminous pulses (ionizing waves) that move with speeds of 106--107 m/s. Because of the complexity of the fluid equations, the usual attempts to find shocklike solutions use numerical methods. In an attempt to find analytical solutions, we have reduced the original system of electron fluid equations (continuity, momentum, and energy conservation) and Maxwell's equations to single nonlinear differential equations. These model equations were solved analytically. Here, this analysis is improved by including a source of electrons due to collisional ionization, as well as the term that takes into account the changes in the cross-sectional area of an ionized channel. In order to be consistent with the concept of a weakly ionized gas, the source term has to be small. The dominant force term that controls the wave motion (in or against the externally applied electrical field, as observed experimentally) is still the electron pressure gradient. The formation, propagation, and damping of electron waves in electrical breakdown of gases are discussed. The results obtained are used to describe the properties and propagation characteristics of a dart leader in lightning. In the fluid dynamical approach, the dart leader is regarded as a compressional wave in an electron fluid component, produced by a rapid charge accumulation at the top of a lightning channel. It moves toward the earth along a decaying channel, formed by a return stroke, with speeds of 106 to 3¿107 m/s. The speed is shown to be linearly proportional to the electron number density gradient, and inversely proportional to the number density of neutral molecules. Dart leader propagates without significant damping as long as the electron pressure gradient is externally maintained by continuous current flow. The observed luminous extent of a dart leader (on average ~50 m) does not represent its true length. It is interpreted as the result of a collisional ionization in the wake of a dart leader, due to the electron temperature increase at its wave front.