  We analyze an 'up-the-gradient' model for the formation of transport channels
of the phytohormone auxin, through auxin-mediated polarization of the PIN1
auxin transporter. We show that this model admits a family of travelling wave
solutions that is parameterized by the height of the auxin-pulse. We uncover
scaling relations for the speed and width of these waves and verify these
rigorous results with numerical computations. In addition, we provide explicit
expressions for the leading-order wave profiles, which allows the influence of
the biological parameters in the problem to be readily identified. Our proofs
are based on a generalization of the scaling principle developed by Friesecke
and Pego to construct pulse solutions to the classic Fermi-Pasta-Ulam-Tsingou
model, which describes a one-dimensional chain of coupled nonlinear springs.
