  We construct a model of innovation diffusion that incorporates a spatial
component into a classical imitation-innovation dynamics first introduced by F.
Bass. Relevant for situations where the imitation process explicitly depends on
the spatial proximity between agents, the resulting nonlinear field dynamics is
exactly solvable. As expected for nonlinear collective dynamics, the imitation
mechanism generates spatio-temporal patterns, possessing here the remarkable
feature that they can be explicitly and analytically discussed. The simplicity
of the model, its intimate connection with the original Bass' modeling
framework and the exact transient solutions offer a rather unique theoretical
stylized framework to describe how innovation jointly develops in space and
time.
