  Ensemble averages of a stochastic model show that, after a formation stage,
the tips of active blood vessels in an angiogenic network form a moving two
dimensional stable diffusive soliton, which advances toward sources of growth
factor. Here we use methods of multiple scales to find the diffusive soliton as
a solution of a deterministic equation for the mean density of active
endothelial cells tips. We characterize the diffusive soliton shape in a
general geometry, and find that its vector velocity and the trajectory of its
center of mass along curvilinear coordinates solve appropriate collective
coordinate equations. The vessel tip density predicted by the soliton compares
well with that obtained by ensemble averages of simulations of the stochastic
model.
