  Recently, numerical simulations of a stochastic model have shown that the
density of vessel tips in tumor induced angiogenesis adopts a soliton-like
profile [Sci. Rep. 6, 31296 (2016)]. In this work, we derive and solve the
equations for the soliton collective coordinates that indicate how the soliton
adapts its shape and velocity to varying chemotaxis and diffusion. The vessel
tip density can be reconstructed from the soliton formulas. While the
stochastic model exhibits large fluctuations, we show that the location of the
maximum vessel tip density for different replicas follows closely the soliton
peak position calculated either by ensemble averages or by solving an
alternative deterministic description of the density. The simple soliton
collective coordinate equations may also be used to ascertain the response of
the vessel network to changes in the parameters and thus to control it.
