  We derive a set of minimal yet complete nonlinear field equations describing
the collective properties of self-propelled rods from a simple microscopic
starting point, the Vicsek model with nematic alignment. Analysis of their
linear and nonlinear dynamics shows good agreement with the original
microscopic model. In particular, we derive an explicit expression for the
fronts forming density-segregated, banded solutions, allowing us to develop a
more complete analytic picture of the problem at the nonlinear level.
