Analytic Scaling Solutions for Cosmic Domain Walls

A relativistic generalization of a well-known method for approximating the dynamics of topological defects in condensed matter is constructed, and applied to the evolution of domain walls in a cosmological context. It is shown that there are self-similar ``scaling'' solutions, for which one can, in principle, calculate many quantities of interest without recourse to numerical simulations. Here, the area density in the scaling regime is calculated in various backgrounds. Remarkably good agreement with numerical simulations is obtained.