  A language dynamics model on a square lattice, which is an extension of the
one popularized by Abrams and Strogatz [1], is analyzed using ODE bifurcation
theory. For this model we are interested in the existence and spectral
stability of structures such as stripes, which are realized through pulses
and/or the concatenation of fronts, and spots, which are a contiguous
collection of sites in which one language is dominant. Because the coupling
between sites is nonlinear, the boundary between sites containing speaking two
different languages is "sharp"; in particular, in a PDE approximation it allows
for the existence of compactly supported pulses (compactons). The dynamics are
considered as a function of the prestige of a language. In particular, it is
seen that as the prestige varies, it allows for a language to spread through
the network, or conversely for its demise.
